How do you get your name off of a car loan that you have cosigned?

One way is to have the other party apply for credit in his/her name and payoff the loan for which you co-signed. By doing this your obligation as a debtor has been fulfilled.

If the other party is unable to obtain credit alone and they are willing to do so, the lender may be willing to substitute you as the co-signer for a person of equal or greater credit worthiness.