A shed would work great! We have some friends who have done that same thing - they just fitted in some roosting areas and put some nest boxes in about a foot off the ground. It's easy enough to lock them up at night, and since her shed is on a cement slab, it's really easy to clean. I think they put a few windows in so it's not so dark if they don't let the chickens out some days. I've heard of other people building in a sort of skylight or using corrugated plastic for roofing to help let in light.

We inherited our coop, so I can't complain, but it's not the best set up for the birds. It has chicken wire on 3 sides, so they would get very cold in winter if we didn't cover it with several layers of thick plastic and keep it in a very protected part of the yard. We're about to have to move it to the backyard area, and I'm probably going to cover 2 of those sides with plywood, maybe with a few cut outs for light. I was thinking of elevating it, but I'm afraid the wind coming up from underneath in winter would be too much for them.

I saw a great little coop once that had grooves to cover the chicken wire with plywood in winter, and you could stuff straw in the gap to insulate it.