There's no reason why you can't have quail in a coop. Just personal preference I think. I personally would like it to be as natural as possible.
Do a search on raising quail in you tube. There's one italian guy who has some great ideas. If your coop has a nesting box. modify them to suit your quail (this is what I'm doing). I'll be having mine on the ground at first to see how they go. This way I can move it around to suit the weather. I haven't made up my mind on whether t have the wire on the floor as well, just to keep unwanted guests out, but then, I'd like them to be able for fetch the worms too, so dunno.