I do that everytime when i need to play my friend's game.
Step 1: close hayday
Step 2: open game center
Step 3: sign out from current game center id used
Step 4: sign in using the gc id you want to play
Step 5: open hayday
Step 6: wait for about 3 seconds, then a pop-up message will appear: "would you like to load game from this game center account?....etc......"
Step 7: tap on "YES"
IMPORTANT: If you're using FB and GC together, make sure that you are using the right FB account for the current GC id you're using or you might lose your game.
To do that log out the wrong FB account then log in to the right FB account that's connected to your GC ID.
Happy farming!
-niktot (lv35)