How do you repossess a car from someone who defaulted on a promissory note in a private sale?

A private auto sale is considered a contract. As such, if the buyer isn't paying as agreed, he's in breach of ths contract and subject to civil remedy, such as a law suit. Unless specified in the contract or allowed by your local law, you can't take the property back. That places you in breach as well and could be considered auto theft.