Can a stop payment be initiated by the purchaser of a bank check or bank money order?

No, neither one can. They can be counterfeit though.
This isn't making sense. If you are the buyer, why are you worried about being paid?
When you buy a car you either hand over green cash after seeing the title and no liens on it and proof that it belongs to the person selling it, by seeing an ID
OR
You meet at the seller's bank and the buyer bankwires the funds while the bank faxes a copy of the title, after which he hands over the title. The buyer would set up the bankwire in person at his bank because he will have to sign a form.