I also put "What kind of car do you have?" and it wasn't accepted. I'm now thinking, though, that maybe that would be "Vad för en bil har du?"
vilken, vilket, vilka is usually just what/which one so I think that Swedish sentence is not asking for the brand or make of car. I struggle to think of a situation where I would ask "what car" and not mean "what make/type/brand of car", though.
Using the other translation of vilken to basically say "Which car is yours?" i.e. there are a few there and you don't know which one belongs to the person you're speaking to, I believe the Swedish *Vilken bil är din?" would be better.
Bottom line is - I don't quite understand why the sentence is translated as it is and why "What car do you have?" is not the same as "What kind of car do you have?"
Any contributors out there? Should it be added maybe?
Edit: "Which car do you have?" is accepted but that, too, sounds rather strange to me.
I live in the American southwest. We use this question frequently before asking for some kind of favor or errand when the person has access to multiple vehicles -- if you have the ranch truck, could you pick up hay or feed; if you don't have the minivan, you can't pick up the children from school for lack of child safety seats; if you have "my" car, could you check to see if I left my sunglasses; if my son is riding in his friend's car, I may not ask them to stop at the pharmacy to pick up a prescription . . .