Anyway this can be done in a coop? I know the roof rack very rarely comes up. Any other solutions?

Yes, I used a large carry bag with the front wheel detached; it fits on the back seat with a little swearing. But don't expect to put people on the back seat too, and I don't recall whether I ever tried with two bikes - I suspect one is the limit.

Another option is to mount it on the roof with those suction cup bike mounts.

Mine had a bike rack on the back before I bought it. It scratched the paint and it needed touching up.
Also the indicator beeps like you are towing a trailer which is annoying but you only think of sorting it when the indicator is on!

Actually, I recall I also used to use a generic external carrier that hooked onto the boot lid. That would carry two bikes but the fuel economy fell through the floor from the extra drag.

Similar experience here with generic boot bike carriers and scratches on the car. Never really noticed fuel economy impact though

There is a thread on here from year's ago about a Paddy Hopkirk one that fits the back, I bought one and used to carry one bike on it...anymore and it would probably deform the boot lid at speed, never had any problems, no paint rub etc.

Like the suction cups above, but downside is headroom.... my mate drove under/into a car park height barrier with his C60 on the roof and totalled the frame and roof of his car, when he forgot what he had put on his roof! Also if MTBing all the shit from the bike goes all over the roof, rear window etc

Thanks for all the help. Love the look of the suction cup racks - there seems to be some very good reviews of them and they're not too dear. However, I'm paranoid about all things to do with the coop, so god knows what I'd be like with a bike on the roof only attached by a little rubber suction cup!

I'll pop down to Halfrauds in the morning and see if they have a rear mounted rack which might fit.