This experience is in one of prior threads as well. I tried, and even told the dealer that I intended to pay with my Amex, in our e-mail conversations. When I went to get the car, the dealer balked. I guess he didn't think I was serious. I very seriously considered walking out of the dealer then and there, but I knew the vehicle with configuration I wanted was in very limited supply in the area and I didn't think I could find another. I ended up charging only the deposit.
In the process, I did contact Amex to make sure the charge would be accepted. They had to do some paperwork, but got it set up fairly quickly.
Some of the car sites (cars.com, carsdirect.com, etc.) showed the Amex symbol on their site at the time. I don't know what happens in those cases if you buy a call from them.