This is a reasonably thorough article on how to raise rabbits in a very small space.
Think keeping rabbits in a chest of drawer size hutch.
I've done this, in exactly this size space. It has lots of benefits, including a very good fertilizer, rabbit fur and Quiet animals
http://www.backdoorsurvival.com/raising-meat-rabbits-small-spaces/Don't forget the food aspect, but remember that rabbits are very low fat and SHOULD NOT be your sole source of meat. You need fats in your diet.