Even neutered and spayed bunnies may find couches and beds tempting. It can mean they are claiming it but it can also mean that they feel they are part of the human herd too. (so they are claiming it still, but it’s not necessarily in competition with you..more like, I’m on your team) LOL.
So wherever your scent is the strongest, like on the couch, it may be fair game to them. Jack, who has been neutered for years would still pee on the couch, but I supervised very closely and the moment I would see him lift his tail, I’d shoo him off. It took some major supervision and persistence….and patience! (of feeling like a broken record), but he no longer will pee on the living room couch even when he is not supervised.
However, this year, he’s begun peeing on the futon in the bunnyroom if I’ve been hanging out on it for awhile. I think he actually does claim to say…MINE, not yours. (as really, the bunny room is their space). I think because he started to realize I wasn’t in there to supervise, he just could do what he wanted. Since I can’t supervise that area as much, I cover the area on the couch that he pees on — right in the seem between the horizontal cushions and where the back of the couch meets. I actually use a thick plastic runner from home depot as he chews holes in thin plastic and then pees over that. NICE!