Interesting idea - is there a minimum rental period so you can establish that "YES, WE LOVE CHICKENS!" that you can basically win everyone over then make what you want? May be a good compromise if the family is on the proverbial fence.
The run I built was a fraction of the cost of the coop, so that might be an option for you - and it required basic skills, whereas our coop had some trickier angles, etc. I'll post a pic of mine and can share more info on it if you like. My husband didn't enjoy some of the process (we each know enough to want to do things differently sometimes), but now that it's finished I catch him outside in a chair talking to them from outside the run