iOS 9 game center doesn't login and the settings for game center won't load ... After backing up my data to iCloud (without games data, mostly the important data like whatsapp and few others), then I restored from iCloud backup ... Game Center started to login back again, with delay however..
The ultimate solution would be an update or fix from Apple themselves.
Please join the Game Center issue discussion to followup the issue updates and hopefully the solution ( https://discussions.apple.com/thread/... )