I have no experience with rabbits and cats, however there are quite a few youtube videos showing cats and rabbits interacting. I’d like to think that a cat and rabbit sharing a house would get along especially if the two are about the same size. Although rabbits can go into shock when faced with a unknown predator, I think when rabbits become familiar with a cat or dog of about the same size, they will defend themselves.
We have a pen, about 3 feet by 6 feet for our two Flemish rabbits. It’s in our living room. They’ve used it since they were about 2 months old. At first we would herd them back into the pen whenever we went to bed or left the house. It was usually a struggle to get them back into the pen…they didn’t want to be penned up. Later they began fighting at night, so we stopped penning them at night. We just let them stay outside the pen where ever in the living room they wanted to be. They are going on 7 months old now, The pen door has been continuously open for over three months. Now that they aren’t forced to be in the pen, they spend quite a bit of time in there. I guess knowing that they are perfectly free to come and go, makes them very relaxed about voluntarily going in there.
The pen does have a covered top, so I think they feel safe in there. They often lay under the coffee table. We have several cardboard boxes under a dining room table, which is pushed up against a wall, they like to stay under the table being hid behind the boxes. They like to play with the boxes, push them around, jump in the boxes, and eat the boxes!