UIPageViewController page control background color

You can use appearance to change the color of UIPageControl as otherwise it is not accessible. Try doing it in your AppDelegate's didFinishLaunchingWithOptions function as given below.

- (BOOL)application:(UIApplication *)application didFinishLaunchingWithOptions:(NSDictionary *)launchOptions
{
    UIPageControl *pageControl = [UIPageControl appearance];
    pageControl.pageIndicatorTintColor = [UIColor lightGrayColor];
    pageControl.currentPageIndicatorTintColor = [UIColor blackColor];
    pageControl.backgroundColor = [UIColor blueColor];

    return YES;
}

To apply style only to a particular view controller, you can use appearanceWhenContainedIn instead as following:

UIPageControl *pageControl = [UIPageControl appearanceWhenContainedIn:[MyViewController class], nil];

Only UIPageControl objects contained in the MyViewController are going to get this style.

EDIT: The black background around UIPageControl at the bottom of your screen is due to the background color of your UIPageViewController not UIPageControl. You can change this color as following:

- (void)viewDidLoad {
    [super viewDidLoad];
    self.view.backgroundColor = [UIColor blueColor]; //Set it to whatever you like
}

Updated for Swift 3:

override func viewDidLayoutSubviews() {
    super.viewDidLayoutSubviews()
    for view in self.view.subviews {
        if view is UIScrollView {
            view.frame = UIScreen.main.bounds
        } else if view is UIPageControl {
            view.backgroundColor = UIColor.clear
        }
    }
}

Swift 2 example for anyone that needs it. Put this inside your UIPageController subclass.

override func viewDidLayoutSubviews() {
    super.viewDidLayoutSubviews()
    for view in self.view.subviews {
        if view is UIScrollView {
            view.frame = UIScreen.mainScreen().bounds
        } else if view is UIPageControl {
            view.backgroundColor = UIColor.clearColor()
        }
    }
}

Add the following code in the UIPageViewController.

- (void)viewDidLoad {
    [super viewDidLoad];
    [[UIPageControl appearance] setPageIndicatorTintColor: [UIColor grayColor]];
    [[UIPageControl appearance] setCurrentPageIndicatorTintColor: [UIColor whiteColor]];
    [[UIPageControl appearance] setBackgroundColor: [UIColor darkGrayColor]];
}

Just subclass UIPageViewController and add this code:

- (void)viewDidLayoutSubviews {
  [super viewDidLayoutSubviews];
  for (UIView *view in self.view.subviews) {
    if ([view isKindOfClass:[NSClassFromString(@"_UIQueuingScrollView") class]]) {
      CGRect frame = view.frame;
      frame.size.height = view.superview.frame.size.height;
      view.frame = frame;
    }
  }
}

This will extend internal scroll view frame.

Here is the Swift 2+ version of Yas-T's Answer

//In AppDelegate
let pageControl = UIPageControl.appearance()
pageControl.pageIndicatorTintColor = UIColor.lightGrayColor()
pageControl.currentPageIndicatorTintColor = UIColor.blackColor()
pageControl.backgroundColor = UIColor.blueColor()

//Or in your ViewController (Only available on IOS 9.0)
if #available(iOS 9.0, *) {
   let pageControl = UIPageControl.appearanceWhenContainedInInstancesOfClasses([ViewController.self])
   pageControl.pageIndicatorTintColor = UIColor.lightGrayColor()
   pageControl.currentPageIndicatorTintColor = UIColor.darkGrayColor()
}