what's the best way to accomplish the above in the state of NY, where we both currently live if the car is registered in my name to the state of NJ?
The procedure would be the same as is you sold the vehicle. You would have to sign the title over and she would register in New York. You would then have to file a lien against the vehicle. I caution you that having her take of the payments will not absolve you of ultimate responsibility for the payments should she default. I urge you to speak with an attorney to explain the legal ramifications of what you are trying to do, review and advise you of the proper documents to complete and to verify that all documentation is properly filed to secure your interest in the vehicle.