How do I find out which Game Center account a game is tied to? I played Clash of Clans one year ago and I have many game center accounts.

My problem is that I forgot which game center account has my game progress. How do I know which registered account is linked with Clash of Clans?
The only way to find out is to login with every known account.  Gamecenter accounts are easily changeable and doing so doesn't affect the rest of your device because your Apple-ID/iCloud login is seperated from your Gamecenter account.

While Supercell, the developer of CoC is very helpful when you have account issues, it is impossible for them to look it up for you.  Gamecenter and other game related data is not stored under your Gamecenter email ID.  It is stored using a hashed number, visually unrelated with your real human readable login credentials.

If - perhaps long time ago - you contacted Supercell about any issues, they might have your hash-id in their archives.  If not, the only option you have is to manually try them all.