Mine do poop when they sit on a roost , otherwise they don't poop in coop either. If my chickens ( the young ) sleep in a nestbox without being broody, they poop in it too. I don’t like that bc eggs get smeared and it’s more work to clean.
I always trained chickens who wouldn’t roost by themself. Putting them on the roost or blocking the nest in the evening.
Your chickens have roosted in trees before. So the sure know the concept. If they don’t use the roost now, there is probably something wrong with it. The roost must be higher than the nestbox to start with. Many prefab coops come with roosts/nestboxes in a wrong spot. Often too many nestboxes , not enough height and a poor layout out with lousy ventilation. Maybe it helps if you make the roost bar as heigh as possible. Or make a nestbox (fake egg in a pot) on the floor to lay their eggs. Close the two nestboxes in the coop. Try for a week if it doesn’t work try something else.
I know people who took out the bottom of the coop to gain roost hight inside the coop, and somehow lowered the nest-boxes.
I extended my coop/run with a roost area. My chickens kept using the 2 nestboxes in the tiny coop and preferred to sleep in the new extension which I originally made as a shelter to use during the day. I added photos to get a better idea.
Higher roost:
View attachment 4106940
Original coop with small run:
View attachment 4106939
And later with the extension built on the right (in front) .
View attachment 4106942