My dog crates have a plastic tray in the bottom. I use bedding -- pine shavings. I use deep layer method in the coop and a modification in the dog crates -- the deep layer in the coop is 6'-8" deep and I can only keep a 2"-3" layer of bedding in each crate. So many days, I leave the bedding to dry during the day when the ducks are out in the back garden and then scoop out any particularly poopy messes and put another layer of pine shavings on top of the wet bedding. I am then raking out the bedding in the crates every 7-10 days.
My coop has hardware cloth bottom and I use a layer of leaves on top of the hardware cloth and then pine shavings, so that the little feet were not harmed when we hade cold weather [I am in E Florida so "cold weather" is relative, I gave the ducks pine straw bales to prevent draughts and pulled out pine straw [long pine needles] for the ducks to snuggle up in. The pine straw got added to the deep layer bedding, too and added more protection from the now deeply buried hardware cloth.