When going to work, two cats are left alone in the house. When coming home at night, there's a big mess on the floor. The only solution so far has been to put the aggressive cat inside a cat carrier for a portion of the day/night to allow the meeker cat the opportunity to use the litter box.
The next solution is to possibly make the more aggressive cat an outdoor cat, but that might not be fair. What can be done to curb bullying where one cat won't let the other cat use the litter box?
Add a second litter box to the house.
It is not unusual for any animal to get overly protective of 'their' litter box. I have seen this behavior in both cats and rabbits. It is generally solved by adding a second litter box some distance from the first. While the more aggressive pet might want to protect both boxes, it is logistically difficult to do so if they are well separated.
There are many variables, but either both pets will start sharing both boxes, or one pet will use one exclusively while the more dominant pet will use both. In either case, there will be adequate facilities available.
There may be other behavior issues that need to be addressed as well you can find related questions here
Unless you've directly observed one cat bullying the other over use of the litter box, one possibility is that the more aggressive cat is simply using the litter box that appears cleanest / most convenient at the time. While some cats are very fussy in that regard, we've got one cat that doesn't seem to care much if the litter box has been used by another cat and uses whichever one is closest, while the others refuse to use it once that has occurred.
If that sounds like a possibility, the main option that comes to mind is to provide maybe two or three litter boxes and see how it goes. In my experience most cats don't tend to go out of their way to mark their territory like many dogs do.
If the more aggressive cat has a few favorite spots, maybe place a litter box or two near those areas and place another in a less convenient area, and maybe there'll be less contention over who gets to use each one. That may also help if there is direct bullying, because the more aggressive cat may be less aware that the other cat is using the litter box if it's a distance away from where he/she normally hangs out.
I'm going to make some assumptions here - that you've observed the aggressive cat preventing the other cat from approaching the litter box or otherwise bullying the more timid cat, and that the two cats aren't getting on terribly well.
In this situation, your best bet is to make a closable room a refuge for the timid cat (similar to what's recommended to stop middening). The room will need a selection of cat toys for your timid cat, a lot of things that smell of you, and a litter box, food, and water.
You'll need to spend plenty of time in the room with the timid cat (if you have a study with a closable door, this is perfect). You'll also want to provide a place in the room where the timid cat can hide and feel safe. The recommendations for middening are that it will usually take a week or so for the cat to relax. You will want to change the items in the room around a bit (you want to make sure the timid cat is relaxed even with items that smell of the aggressive cat).
In time both cats should start getting lonely and trying to play with each other by poking paws under the door. At this point, you can bring the timid cat out for some supervised time in the aggressive cat's company. If the aggressive one starts bullying, take the timid one back to the sanctuary, and leave both alone for a while (you don't want the timid cat associating being bullied with getting your attention any more than you want the aggressive one associating bullying with getting your attention). Rinse and repeat until both cats are relatively calm in each others presence.
If this method fails, then the last ditch is to get one of those expensive cat doors with a key and put the cat door in the door to the timid cat's sanctuary. The timid cat gets to wear the collar with the key so it has somewhere to go that the aggressive cat can't reach it. As long as the timid cat has litter, food, water, and toys in there, you shouldn't have any more messes.
Put another litter box far enough from the first so a single cat can't 'monopolise' it, possibly in another room out of vision-line from the first.
