Sail,
Oh, yes, chickens poop just anywhere! And frequently! You can put a slanted board under the roost that catches most of the poop. You can make it removable or stationary (in which case you scrape). If the coop is to be mobile, you can move the coop, scoop the poop and put it on the compost pile.
Don't we have fascinating conversations here on the Farm Life forum?

I suppose they can't be potty trained??? :)

I will incorporate a removable plastic tray into the design and see how that works out.

Honey, if you can potty train chickens, take your show on the road and make a bundle! I personally would hire you to train my flock. I love my girls, but not only do they lack table manners, but their bathroom habits need upgrading, also.
A removable plastic tray should work fine (also easier to hose off if necessary).
Your hens will be fine, happy, and you'll enjoy them immensely. My husband says watching the girls is better than reality TV.

I had seen a pit on a website and have used a plastic bin under my roosts.This worked great.I just added shredded leaves or sawdust on top and it didn't smell bad...a couple of my hens layed next to it and I moved it(it had been a while since I emptied it!)The mice exploded out of it,behind it,they were even nesting in it!I took it out and am catching mice now-up to 20 so far.When I put it back,I will be sure to empty it regularly.Posy_Pet

If your making it mobile, just put rabbit wire as the floor and let droppings fall to the ground. Or make the floor slatted , of course droppings will fall tru the wire easier. Youll need to take a wire brush to the wire once in a while but its easier than having to empty some container.
josh