I recently bought a car and they were happy to let me put up to 100% of the purchase on a card so long as I paid the card processing fee (something like 2 or 3%).

I think they can just run it as debit. That's what they did for my down payment when I bought a new vehicle this past June.

My regular dealership even has a card surcharge for service these days. Given the rebate I get it's pretty much a no-care for smallish bills. But when I bought the car from another dealer was a bit surprised I didn't need to run to the bank to get a certified check.