You probably would not be successful in that type of suit since a co signer has the same responsibility to make payments as the primary buyer. The primary buyer would be able to use the auto loan contract as a defense, saying that you made an agreement with the loan company to make the payments.
If you are looking to get out of the loan, you should encourage the primary buyer to try to refinance. If he or she can get approved individually, then you can get out of the loan free and clear.
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If your role was primarily as a guarantor of the loan, and the other person is the "owner", I think you do have rights against her or her to collect payments you have made. If you are a co-owner of the vehicle, you would not. You need to speak with a lawyer in your area who handles collections or civil litigation to deterrmine how best to proceed.
If you co-signed or guaranteed the loan then you are equally liable to the creditor so you have no defense to payment. As between your co-obligor, if you pay more than fifty percent of the obligation you can sue him for contribution for any amounts in excess of fifty percent of the debt. If the other person is the obligor and you are a guarantor you may have a claim for indemnification against him/her.