Add UIPickerView & a Button in Action sheet - How?

One more solution:

• no toolbar but a segmented control (eyecandy)

  UIActionSheet *actionSheet = [[UIActionSheet alloc] initWithTitle:nil 
                                                      delegate:nil
                                                      cancelButtonTitle:nil
                                                      destructiveButtonTitle:nil
                                                      otherButtonTitles:nil];
  
  [actionSheet setActionSheetStyle:UIActionSheetStyleBlackTranslucent];
  
  CGRect pickerFrame = CGRectMake(0, 40, 0, 0);
  
  UIPickerView *pickerView = [[UIPickerView alloc] initWithFrame:pickerFrame];
  pickerView.showsSelectionIndicator = YES;
  pickerView.dataSource = self;
  pickerView.delegate = self;
  
  [actionSheet addSubview:pickerView];
  [pickerView release];
  
  UISegmentedControl *closeButton = [[UISegmentedControl alloc] initWithItems:[NSArray arrayWithObject:@"Close"]];
  closeButton.momentary = YES; 
  closeButton.frame = CGRectMake(260, 7.0f, 50.0f, 30.0f);
  closeButton.segmentedControlStyle = UISegmentedControlStyleBar;
  closeButton.tintColor = [UIColor blackColor];
  [closeButton addTarget:self action:@selector(dismissActionSheet:) forControlEvents:UIControlEventValueChanged];
  [actionSheet addSubview:closeButton];
  [closeButton release];
  
  [actionSheet showInView:[[UIApplication sharedApplication] keyWindow]];
  
  [actionSheet setBounds:CGRectMake(0, 0, 320, 485)];
  

Even though this question is old, I'll quickly mention that I've thrown together an ActionSheetPicker class with a convenience function, so you can spawn an ActionSheet with a UIPickerView in one line. It's based on code from answers to this question.

Edit: It now also supports the use of a DatePicker and DistancePicker.

UPD:

This version is deprecated: use ActionSheetPicker-3.0 instead.