At the moment, the only other method besides a Facebook account is to save your progress or synchronize your progress across devices is Apple ID.
Other services or methods for saving your game are unfortunately not available right now.
In the meantime, if you need to restore lost progress or move your progress entirely to a new device but can't use Facebook or Apple ID, we may be able to help. What we will need in order to do this is your Support ID. This can be found in the game under Menu > Support > Contact Us > Copy Support ID - tapping on that will enable you to paste it into your email.