How to document a "deposit" on a private party sale?

You can simply write it down on a slip of paper with all the terms and conditions and you'll be fine .... IF both purchaser and buyer sign it! Make 2 copied and you both sign both, you keep one, they keep one.

Include vehicle description, VIN, currently titled to... and actually, the true owner is the one who really should sign it, unless you have power-of-attorney.