I paper trained a rooster. Sort of. Back when I began my flock, I ended up with a rooster out of a batch of Wyandotte pullets. My run was too small for a partitioned area for this fellow, and he needed to be separate as he was a maniac with the hens. So he would spend days outside the run.
This became impractical when winter came. It was too cold and miserable to leave him out, so I brought him into the garage. He was in a dog crate most of the time, but periodically, I would take him out and place him on a newspaper on a window shelf. He would poop, and then I would put him back in the crate. He wasn't abused, he did spend time with the hens, so he wasn't deprived of all chicken companionship and he roosted every night with the flock.
Stan the Wyandotte
Roosters are quite smart. They easily learn their name and respond to it, respond to discipline, so it follows that they could probably be paper trained as you would a puppy.
Begin by confining him to a paper in a small space as you would a puppy. Then expand his space to include bare floor. If he is about to squat on the bare floor, as you would a puppy, you move him quickly onto the paper. Chickens are creatures of habit, and I imagine it wouldn't take long to house break or paper train a roo.