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
}