My parents used their credit card for a deposit on their Honda Civic in Dec. '06. No issues there, so talk to the general manager.
With a good reputable BMW dealer, locating a car from another dealer is fine. I did a referral for a friend who wanted a 325i back in March '06. My sales rep did a dealer exchange at port for the 325i that they wanted and my friend paid $800 over invoice.
With my uncle, it's another story. The sleazy dealer in NYC claimed to have located an Acura MDX they wanted and said they would have it within the month. He put down a deposit, and the car never came. It was a classic case of dealer pressure. The dealer kept pushing them to take another MDX with more options they currently had on the lot. They ended waiting for 2 months and then paid more for the MDX on the lot. Had I been there and done all the negotiations for them, I would have given that dealership a piece of my mind for ripping off my uncle!
Back OT, I would definately talk to the manager; unless you've maxed out your card, I don't think there's a reason why they can't put the deposit on a CC. Otherwise, go elsewhere. There are many honest dealers willing to do business with folks.