OK..I found a solution....I was going through the same thing, here's what I did.

Phone I play on: Samsung Galaxy Note 1 (yea it's old...don't judge)

1. Go on your phone or android device and open CoC and wait for it to load.
2. Go to settings in the bottom right corner.
3. I you are currently disconnected the skip, if you are connected then disconnect under settings by pressing Google+ Sign-In
4. Go to Google and create an account that you will use to back up CoC or any other game you have on your device. (for example: [email protected])
5. Go into settings (the phones settings or your android device settings)
6. Go to accounts and click on the account that is currently backing CoC.
7. On the bottom of the screen select "Remove account" It will read "Removing the account will delete all of its messages, contacts, and other data from the device. Continue? Select Remove account.
8. Go on your phone or android device and open CoC and wait for it to load.
9. Go to settings in the bottom right corner.
10. Under settings press Google+ Sign-In
11. Use the account information you created in step 1
12. Follow all on screen directions.
13. After your game is backed up go into settings (the phones settings or your android device settings)
14. Go to accounts and select "add account"
15. Select Google and select existing.
16. Put in your previous account that was removed in step 4. (This account will be associated with your previos apps except CoC
17. Make sure to sync you of your current accounts.
18. Let me know how this goes.

Good Luck!

Note: Your current village will now be associated with the new account in step 1. The old village will still be associated with the old account.

I hope this help

OK..I found a solution....I was going through the same thing, here's what I did.

Phone I play on: Samsung Galaxy Note 1

1. Go on your phone or android device and open CoC and wait for it to load.
2. Go to settings in the bottom right corner.
3. I you are currently disconnected the skip, if you are connected then disconnect under settings by pressing Google+ Sign-In
4. Go to Google and create an account that you will use to back up CoC or any other game you have on your device. (for example: [email protected])
5. Go into settings (the phones settings or your android device settings)
6. Go to accounts and click on the account that is currently backing CoC.
7. On the bottom of the screen select "Remove account" It will read "Removing the account will delete all of its messages, contacts, and other data from the device. Continue? Select Remove account.
8. Go on your phone or android device and open CoC and wait for it to load.
9. Go to settings in the bottom right corner.
10. Under settings press Google+ Sign-In
11. Use the account information you created in step 1
12. Follow all on screen directions.
13. After your game is backed up go into settings (the phones settings or your android device settings)
14. Go to accounts and select "add account"
15. Select Google and select existing.
16. Put in your previous account that was removed in step 4. (This account will be associated with your previos apps except CoC
17. Make sure to sync you of your current accounts.

Good Luck!

Note: Your current village will now be associated with the new account in step 1. The old village will still be associated with the old account.