Changing login credentials

Is it possible to convert my login from using Google credentials to Github credentials?

I have to login to other sites using a different Google account (given by my university) than the Google account I used for CodeAbbey. Now when I reach the site and click the Google button to login, it uses my university credentials and shows that I have no progress.

The only "fix" is to dump my cookies, forget previous Google logins and come back to CodeAbbey. That's super annoying!