The only way to login to your account on another device, or after deleting your app, is to login with Game Center or Google Play Services. Please be signed in with your Game Center/Google Play Services account, and then start Fun Run Arena. Since there is no other way of signing in to the game, it is very important to connect your Game Center/Google Play Services account to your Fun Run Arena account. This is done the first time you start the app or in the Settings screen. Previously it was possible to connect via Facebook, but this option has been removed.
I still can't login to my old account!