So we all know Game Center isn't ideal - if user's don't login at install time it can be hard to get them to login whilst within your app. Game Center is designed to stop presenting the Game Center login view after the user has dismissed it a few times. Short of giving the user clear instructions to login once this has occurred there isn't really any ideal solution to get your user to login once they have decided to do so.
Well, until now - faced with this issue I looked into suitable solutions and found this little snippet which allows you to open the Game Center app from your own. Now I know this means they will leave your app and need to return but it does take all the guess work out of will they or won't they see the Game Center login view.
[[UIApplication sharedApplication] openURL:[NSURL URLWithString:@"gamecenter:"]];