Problem with my dog getting into litter box.?

We have 2 cats and 1 dog. My dog is a yorkshire terrier and he is the same size as the cats - if not a little smaller by the time the cats mature. The cats have their own room which is wedged open for them to get in. The problem is that since the dog is the same size as the cats he is getting in there as well. We think he only does it when we are not around but we still can see the litter on his mouth. Our cats aren't really jumpers so getting them to jump in the room isn't an option. Does anyone have any suggestions of how we can make it so only the cats can get in their room and the dog stays out? We live in an apartment so we can't really alter doors and stuff like that. Also, we don't want to buy anything that goes into the litter to deter the dog. We just want him to not be able to get in the room at all. Thank you for your help.