Last time I bought a brand new car (~8 years ago?), the dealer told me I couldn't pay more than $X amount, using credit cards, on the car, so I still needed a bank check for the rest (they wouldn't accept a personal check either).
Don't know if things have changed since.
In my experience, it used to be a cashier's check for the balance (if there was a deposit). But a couple years ago at least the dealer I bought from was fine with a personal check. Don't know if it was just this dealer or if personal check verification processes have improved.
Haven't they heard of bank transfers? In Europe you can use SEPA and if you warn the bank in advance, they're basically instant even for large amounts.