You know, you could just disable colors already picked in close proximity. For maximum distinguishing power, offer primary colors first, then secondary and tertiary colors, and then differences in brightness/saturation.
Unless you're dealing with several dozen cars arriving at once, it should be reasonably distinct, and even if for some freak reason there is more cars than colors, it'll still help sorting through prospective cars more quickly.
You could also do this automatically, but offering the user control over it may help them feel in charge and/or remember the color they picked better than just assigning one.
That's my thoughts on it.
