Can I transfer game progress for Clash of Clans between GameCenter accounts I downloaded clash of clans on my sisters apple account. I then made my own apple account. When I try purchasing gems I can't because it says something about the app not being downloaded from this apple account.

Is there a way I can't delete clash of clans and then re download it without losing any progress?!! Please help!! I also have a gamecenter account.
Unfortunately no you can't transfer data between Game Center Accounts.  Apple doesn't allow moving data between Apple ID's.