Unfortunately, this is not possible. The link is done on the SuperCell servers, and there's no way to unlink an account from a Google+ (Android) or Game Center account (iOS).
You will need to create a new Google+ account to link to your village.
Just FYI, there's some information I found on Google that suggests you can unlink it by going into Google+ settings. I just tried these suggestions with a test village of mine and can co firm that process doesn't work.
When your Clash of Clans say your Facebook is disconnected, it's usually because your authentication/access token (the one given to Supercell and your client when you were prompted for authentication) has expired. It expires when one of the following happens:
- Your Facebook password was changed.
- You manually chose to deauthorize the app (in your Apps page), simply click the cog wheel and refer to the pop-up box.
- Expires after some time.
You can read up more about Authentication tokens on the Facebook Developers' page.
As for linking with Facebook - It is not possible, as Facebook does not allow for apps to store identification data (not access tokens, client IDs or changable account identifiers), but actual static identifiers (like a SteamID).
So, there is no way to restore without using Games Center (for iOS) or logging with a Google Play (Android) account, as these services do allow the game (or for Clash of Clans' case; their servers) to store a static identifier ID.
Lastly, as for the game saying you're constantly getting disconnected, are you:
- Constantly changing your password/deauthorizing apps?
- Not using the Facebook app or Safari (for iOS), or using the in-built browser(for Android) to do the authentication?
If so, you may want to consider using Safari (for iOS), or for Android devices, a modern browser such as Google Chrome or Mozilla Firefox.
Alternatively, it's the safest to use the Facebook app for both device types as Facebook stores the data on the app too, along with logging-in not being a hassle (in case of cross-browser/app errors).
Best Answer
To connect your village to Google+, open the Google+ app on your device and make sure you are logged in.
After this, open Clash of Clans and go to the in-game setting. Press the Google+ sign in button to connect your village to Google+. The Google+ Button should change from Disconnected to Connected.
See the images below: