UIDatePicker select Month and Year

Here is a solution to get the same effect. For using this snippet of code you should replace UIPickerView to CDatePickerViewEx in nib file in "Custom class" of "Indentity inspector".

.h file

#import <UIKit/UIKit.h>

@interface CDatePickerViewEx : UIPickerView <UIPickerViewDelegate, UIPickerViewDataSource> 

@property (nonatomic, strong, readonly) NSDate *date;
-(void)selectToday;

@end

.m file

#import "CDatePickerViewEx.h"

// Identifiers of components
#define MONTH ( 0 )
#define YEAR ( 1 )    

// Identifies for component views
#define LABEL_TAG 43


@interface CDatePickerViewEx()

@property (nonatomic, strong) NSIndexPath *todayIndexPath;
@property (nonatomic, strong) NSArray *months;
@property (nonatomic, strong) NSArray *years;

-(NSArray *)nameOfYears;
-(NSArray *)nameOfMonths;
-(CGFloat)componentWidth;

-(UILabel *)labelForComponent:(NSInteger)component selected:(BOOL)selected;
-(NSString *)titleForRow:(NSInteger)row forComponent:(NSInteger)component;
-(NSIndexPath *)todayPath;
-(NSInteger)bigRowMonthCount;
-(NSInteger)bigRowYearCount;
-(NSString *)currentMonthName;
-(NSString *)currentYearName;

@end

@implementation CDatePickerViewEx

const NSInteger bigRowCount = 1000; 
const NSInteger minYear = 2008;
const NSInteger maxYear = 2030;
const CGFloat rowHeight = 44.f;
const NSInteger numberOfComponents = 2;

@synthesize todayIndexPath;
@synthesize months;
@synthesize years = _years;

-(void)awakeFromNib
{
    [super awakeFromNib];

    self.months = [self nameOfMonths];
    self.years = [self nameOfYears];
    self.todayIndexPath = [self todayPath];

    self.delegate = self;
    self.dataSource = self;

    [self selectToday];
}

-(NSDate *)date
{
    NSInteger monthCount = [self.months count];
    NSString *month = [self.months objectAtIndex:([self selectedRowInComponent:MONTH] % monthCount)];

    NSInteger yearCount = [self.years count];
    NSString *year = [self.years objectAtIndex:([self selectedRowInComponent:YEAR] % yearCount)];

    NSDateFormatter *formatter = [[NSDateFormatter alloc] init]; [formatter setDateFormat:@"MMMM:yyyy"];
    NSDate *date = [formatter dateFromString:[NSString stringWithFormat:@"%@:%@", month, year]];
    return date;
}

#pragma mark - UIPickerViewDelegate
-(CGFloat)pickerView:(UIPickerView *)pickerView widthForComponent:(NSInteger)component
{
    return [self componentWidth];
}

-(UIView *)pickerView: (UIPickerView *)pickerView
            viewForRow: (NSInteger)row
          forComponent: (NSInteger)component
           reusingView: (UIView *)view
{   
    BOOL selected = NO;    
    if(component == MONTH)
    {
        NSInteger monthCount = [self.months count];
        NSString *monthName = [self.months objectAtIndex:(row % monthCount)]; 
        NSString *currentMonthName = [self currentMonthName];
        if([monthName isEqualToString:currentMonthName] == YES)
        {
            selected = YES;
        }
    }
    else
    {
        NSInteger yearCount = [self.years count];
        NSString *yearName = [self.years objectAtIndex:(row % yearCount)];
        NSString *currenrYearName  = [self currentYearName];
        if([yearName isEqualToString:currenrYearName] == YES)
        {
            selected = YES;
        }
    }

    UILabel *returnView = nil;
    if(view.tag == LABEL_TAG)
    {
        returnView = (UILabel *)view;
    }
    else 
    {
        returnView = [self labelForComponent: component selected: selected];
    }

    returnView.textColor = selected ? [UIColor blueColor] : [UIColor blackColor];
    returnView.text = [self titleForRow:row forComponent:component];
    return returnView;
}

-(CGFloat)pickerView:(UIPickerView *)pickerView rowHeightForComponent:(NSInteger)component
{
    return rowHeight;
}

#pragma mark - UIPickerViewDataSource
- (NSInteger)numberOfComponentsInPickerView:(UIPickerView *)pickerView
{
    return numberOfComponents;
}

-(NSInteger)pickerView:(UIPickerView *)pickerView numberOfRowsInComponent:(NSInteger)component
{
    if(component == MONTH)
    {
        return [self bigRowMonthCount];
    }
    return [self bigRowYearCount];
}

#pragma mark - Util
-(NSInteger)bigRowMonthCount
{
    return [self.months count]  * bigRowCount;
}

-(NSInteger)bigRowYearCount
{
    return [self.years count]  * bigRowCount;
}

-(CGFloat)componentWidth
{
    return self.bounds.size.width / numberOfComponents;
}

-(NSString *)titleForRow:(NSInteger)row forComponent:(NSInteger)component
{
    if(component == MONTH)
    {
        NSInteger monthCount = [self.months count];
        return [self.months objectAtIndex:(row % monthCount)]; 
    }
    NSInteger yearCount = [self.years count];
    return [self.years objectAtIndex:(row % yearCount)];
}

-(UILabel *)labelForComponent:(NSInteger)component selected:(BOOL)selected
{
    CGRect frame = CGRectMake(0.f, 0.f, [self componentWidth],rowHeight);

    UILabel *label = [[UILabel alloc] initWithFrame:frame];
    label.textAlignment = UITextAlignmentCenter;
    label.backgroundColor = [UIColor clearColor];
    label.textColor = selected ? [UIColor blueColor] : [UIColor blackColor];
    label.font = [UIFont boldSystemFontOfSize:18.f];
    label.userInteractionEnabled = NO;

    label.tag = LABEL_TAG;

    return label;
}

-(NSArray *)nameOfMonths
{    
    NSDateFormatter *dateFormatter = [NSDateFormatter new];
    return [dateFormatter standaloneMonthSymbols];
}

-(NSArray *)nameOfYears
{
    NSMutableArray *years = [NSMutableArray array];

    for(NSInteger year = minYear; year <= maxYear; year++) 
    {
        NSString *yearStr = [NSString stringWithFormat:@"%i", year];
        [years addObject:yearStr];
    }
    return years;
}

-(void)selectToday
{
    [self selectRow: self.todayIndexPath.row
        inComponent: MONTH
           animated: NO];

    [self selectRow: self.todayIndexPath.section
        inComponent: YEAR
           animated: NO];
}

-(NSIndexPath *)todayPath // row - month ; section - year
{
    CGFloat row = 0.f;
    CGFloat section = 0.f;

    NSString *month = [self currentMonthName];
    NSString *year  = [self currentYearName];

    //set table on the middle
    for(NSString *cellMonth in self.months) 
    {
        if([cellMonth isEqualToString:month]) 
        {
            row = [self.months indexOfObject:cellMonth];
            row = row + [self bigRowMonthCount] / 2;
            break;
        }
    }

    for(NSString *cellYear in self.years) 
    {
        if([cellYear isEqualToString:year]) 
        {
            section = [self.years indexOfObject:cellYear];
            section = section + [self bigRowYearCount] / 2;
            break;
        }
    }

    return [NSIndexPath indexPathForRow:row inSection:section];
}

-(NSString *)currentMonthName
{
    NSDateFormatter *formatter = [[NSDateFormatter alloc] init];
    [formatter setDateFormat:@"MMMM"];
    return [formatter stringFromDate:[NSDate date]];
}

-(NSString *)currentYearName
{
    NSDateFormatter *formatter = [[NSDateFormatter alloc] init];
    [formatter setDateFormat:@"yyyy"];
    return [formatter stringFromDate:[NSDate date]];
}

@end

Yeah, you probably want to just make your own picker. You don't have to subclass it or anything, though; just use a generic UIPickerView and return appropriate values from your UIPickerViewDelegate/UIPickerViewDataSource methods.

I rewrote Igor's answer in Swift:

class CLIVEDatePickerView: UIPickerView  {

    enum Component: Int {
        case Month = 0
        case Year = 1
    }

    let LABEL_TAG = 43
    let bigRowCount = 1000
    let numberOfComponentsRequired = 2

    let months = ["01", "02", "03", "04", "05", "06", "07", "08", "09", "10", "11", "12"]
    var years: [String] {
        get {
            var years: [String] = [String]()

            for i in minYear...maxYear {
                years.append("\(i)")
            }

            return years;
        }
    }

    var bigRowMonthsCount: Int {
        get {
            return bigRowCount * months.count
        }
    }

    var bigRowYearsCount: Int {
        get {
            return bigRowCount * years.count
        }
    }

    var monthSelectedTextColor: UIColor?
    var monthTextColor: UIColor?
    var yearSelectedTextColor: UIColor?
    var yearTextColor: UIColor?
    var monthSelectedFont: UIFont?
    var monthFont: UIFont?
    var yearSelectedFont: UIFont?
    var yearFont: UIFont?

    let rowHeight: NSInteger = 44

    /**
     Will be returned in user's current TimeZone settings
    **/
    var date: NSDate {
        get {
            let month = self.months[selectedRowInComponent(Component.Month.rawValue) % months.count]
            let year = self.years[selectedRowInComponent(Component.Year.rawValue) % years.count]
            let formatter = NSDateFormatter()
            formatter.dateFormat = "MM yyyy"
            return formatter.dateFromString("\(month) \(year)")!
        }
    }

    var minYear: Int!
    var maxYear: Int!

    override init(frame: CGRect) {
        super.init(frame: frame)
        loadDefaultParameters()
    }

    required init?(coder aDecoder: NSCoder) {
        super.init(coder: aDecoder)
        loadDefaultParameters()
    }
    override func awakeFromNib() {
        super.awakeFromNib()
        loadDefaultParameters()
    }

    func loadDefaultParameters() {
        minYear = NSCalendar.currentCalendar().components(NSCalendarUnit.Year, fromDate: NSDate()).year
        maxYear = minYear! + 10

        self.delegate = self
        self.dataSource = self

        monthSelectedTextColor = UIColor.blueColor()
        monthTextColor = UIColor.blackColor()

        yearSelectedTextColor = UIColor.blueColor()
        yearTextColor = UIColor.blackColor()

        monthSelectedFont = UIFont.boldSystemFontOfSize(17)
        monthFont = UIFont.boldSystemFontOfSize(17)

        yearSelectedFont = UIFont.boldSystemFontOfSize(17)
        yearFont = UIFont.boldSystemFontOfSize(17)
    }


    func setup(minYear: NSInteger, andMaxYear maxYear: NSInteger) {
        self.minYear = minYear

        if maxYear > minYear {
            self.maxYear = maxYear
        } else {
            self.maxYear = minYear + 10
        }
    }

    func selectToday() {
        selectRow(todayIndexPath.row, inComponent: Component.Month.rawValue, animated: false)
        selectRow(todayIndexPath.section, inComponent: Component.Year.rawValue, animated: false)
    }


    var todayIndexPath: NSIndexPath {
        get {
            var row = 0.0
            var section = 0.0

            for cellMonth in months {
                if cellMonth == currentMonthName {
                    row = Double(months.indexOf(cellMonth)!)
                    row = row + Double(bigRowMonthsCount / 2)
                    break
                }
            }

            for cellYear in years {
                if cellYear == currentYearName {
                    section = Double(years.indexOf(cellYear)!)
                    section = section + Double(bigRowYearsCount / 2)
                    break
                }
            }

            return NSIndexPath(forRow: Int(row), inSection: Int(section))
        }
    }

    var currentMonthName: String {
        get {
            let formatter = NSDateFormatter()
            let locale = NSLocale(localeIdentifier: "en_US")
            formatter.locale = locale
            formatter.dateFormat = "MM"
            return formatter.stringFromDate(NSDate())
        }
    }

    var currentYearName: String {
        get {
            let formatter = NSDateFormatter()
            formatter.dateFormat = "yyyy"
            return formatter.stringFromDate(NSDate())
        }
    }


    func selectedColorForComponent(component: NSInteger) -> UIColor {
        if component == Component.Month.rawValue {
            return monthSelectedTextColor!
        }
        return yearSelectedTextColor!
    }

    func colorForComponent(component: NSInteger) -> UIColor {
        if component == Component.Month.rawValue {
            return monthTextColor!
        }
        return yearTextColor!
    }


    func selectedFontForComponent(component: NSInteger) -> UIFont {
        if component == Component.Month.rawValue {
            return monthSelectedFont!
        }
        return yearSelectedFont!
    }

    func fontForComponent(component: NSInteger) -> UIFont {
        if component == Component.Month.rawValue {
            return monthFont!
        }
        return yearFont!
    }



    func titleForRow(row: Int, forComponent component: Int) -> String? {
        if component == Component.Month.rawValue {
            return self.months[row % self.months.count]
        }
        return self.years[row % self.years.count]
    }


    func labelForComponent(component: NSInteger) -> UILabel {
        let frame = CGRect(x: 0.0, y: 0.0, width: bounds.size.width, height: CGFloat(rowHeight))
        let label = UILabel(frame: frame)
        label.textAlignment = NSTextAlignment.Center
        label.backgroundColor = UIColor.clearColor()
        label.userInteractionEnabled = false
        label.tag = LABEL_TAG
        return label
    }
}

extension CLIVEDatePickerView: UIPickerViewDelegate, UIPickerViewDataSource {

    func numberOfComponentsInPickerView(pickerView: UIPickerView) -> Int {
        return numberOfComponentsRequired
    }

    func pickerView(pickerView: UIPickerView, numberOfRowsInComponent component: Int) -> Int {
        if(component == Component.Month.rawValue) {
            return bigRowMonthsCount
        } else {
            return bigRowYearsCount
        }
    }



    func pickerView(pickerView: UIPickerView, widthForComponent component: Int) -> CGFloat {
        return self.bounds.size.width / CGFloat(numberOfComponentsRequired)
    }

    func pickerView(pickerView: UIPickerView, viewForRow row: Int, forComponent component: Int, reusingView view: UIView?) -> UIView {
        var selected = false

        if component == Component.Month.rawValue {
            let monthName = self.months[(row % self.months.count)]
            if monthName == currentMonthName {
                selected = true
            }
        } else {
            let yearName = self.years[(row % self.years.count)]
            if yearName == currentYearName {
                selected = true
            }
        }

        var returnView: UILabel
        if view?.tag == LABEL_TAG {
            returnView = view as! UILabel
        } else {
            returnView = labelForComponent(component)
        }

        returnView.font = selected ? selectedFontForComponent(component) : fontForComponent(component)
        returnView.textColor = selected ? selectedColorForComponent(component) : colorForComponent(component)

        returnView.text = titleForRow(row, forComponent: component)

        return returnView
    }


    func pickerView(pickerView: UIPickerView, rowHeightForComponent component: Int) -> CGFloat {
        return CGFloat(rowHeight)
    }

}

No, this cannot be done using the stock UIDatePicker.

UIDatePickerModeDate

The date picker displays months, days of the month, and years. The exact order of these items depends on the locale setting. An example of this mode is [ November | 15 | 2007 ].

Source: UIDatePicker class reference

I recommend customizing a UIPickerView to use two components and populating its rows with month and year symbols retrieved from NSDateFormatter.