Appreciate this is quite an old thread, but I had the same problem and managed to resolve it by following the steps below. Not sure if the OP is still having the issue, but thought I would post it anyway in case anyone stumbles across the thread.

Steps followed (from memory)

1. Create a test new user account on the Mac
2. Log into that account, configure iCloud (switch off everything apart from Notes sync if you want)
3. See if the permanent syncing issue appears using the test user. If not, then all good - proceed with the steps below.
4. Allow the Notes sync process to complete and stop.
5. Exit Notes.
6. Use Finder to go to ~/Library/Containers/com.apple.Notes/Data/Library/Notes
7. There should be 3 files in this folder. Take a copy of the files and move them to a location you can access using your normal user account (a shared folder or similar).
8. Log out of the test user and back into your normal user account.
9. Shutdown the Notes app if it is running.
10. Navigate to the ~/Library/Containers/com.apple.Notes/Data/Library/Notes folder again.
11. Overwrite the 3 files in this folder with the 3 files taken from the test user account.
12. Start up Notes - hopefully the sync will start and then stop.

Good Luck

Regards

Neil.

I had the same problem and managed to resolve it by following the steps below. Not sure if the OP is still having the issue, but this could assist others finding this thread.

Steps followed (from memory)

1. Create a test new user account on the Mac
2. Log into that account, configure iCloud (switch off everything apart from Notes sync if you want)
3. See if the permanent syncing issue appears using the test user. If not, then all good - proceed with the steps below.
4. Allow the Notes sync process to complete and stop.
5. Exit Notes.
6. Use Finder to go to ~/Library/Containers/com.apple.Notes/Data/Library/Notes
7. There should be 3 files in this folder. Take a copy of the files and move them to a location you can access using your normal user account (a shared folder or similar).
8. Log out of the test user and back into your normal user account.
9. Shutdown the Notes app if it is running.
10. Navigate to the ~/Library/Containers/com.apple.Notes/Data/Library/Notes folder again.
11. Overwrite the 3 files in this folder with the 3 files taken from the test user account.
12. Start up Notes - hopefully the sync will start and then stop.