You didn't say what kind of litter box you have - make sure it's a covered one, if you're not already using a covered one, that right there may help a lot. We have one tiny little cat and we bought a huge litter box for her with a big cover - then we put the litter box in a corner facing the wall - it's kinda caddy-cornered in between a wall and a chair so it creates just a triangle of space - the dogs can't get to it at all & the cat just hops on the chair and then hops down into the little corner & into her litter box.
I tried all other methods I could think of and inevitably we would always forget to put a gate back up, or do something else without thinking, and man those dogs are on top of that quicker than anything. So whatever you do, design it so you no longer are required to "do" something when you leave the room or the house, etc. to prevent the dog from getting in there. Because your dog will continue to try to get at it daily, no matter how much time goes by....