Interestingly, I not long ago tried to pay for a car with a cashier's check and was told that it would not be accepted. I actually had to go open a bank account with it in the locality where I was (the car was a college graduation gift for my son, different state), and as it was Saturday, the bank actually wouldn't trust the cashier's check, either. (They told me that people often try to use forged cashier's checks to establish bank accounts, then immediately use the new ATM card to pull cash before it can be verfied with the issuing bank.) I was only in town for the weekend, so the new bank actually gave me a line of credit for the amount, based on my ability to prove online that I did have well more than the face value in other personal accounts at other banks. We financed the car to get it purchased, and then transferred the money from the new bank account to the loan account the following Monday to pay it off. It was a circus, really.
I have partially paid for car down-payments several times using credit cards, it's something that dealerships tend to think of as an incentive to close the sale that doesn't cost them much, and allowed us to reap travel points (multiples, of course; I time these things carefully). Without exception, the dealerships have limited the CC portion of the downpayment to $2K, and requested a personal check for the rest of it. These days, personal checks can be run through electronic scanners that work to verify the account balance and encumber the amount the same way that a debit card would, but there is no processing fee for those transactions. You cannot do it with a cashier's check, though.