Pigeons, aka squab, are very good eats. Just don't eat street pigeon- skyrats probably aren't good eats. Problem with pigeon is that it is little- best for the soup pot, casseroles, or by the platter. Remember, passenger pigeons were hunted to extinction becuase they congregated in massive flocks and were yummy.

One might also contemplate what my mother, who was raised in Africa, diplomatically calls "small meat". Hamsters, gerbils, and most especially, guinea pigs (big time in Peru). Breed faster than rabbits, take up less space, eat less- heck, they are as close to tribbles as reality allows! Again, best for the soup pot or casseroles, becuase you get about a big sandwich's worth of meat on one of those over sized mice. A big guinea pig might be two pounds, before being dressed; the others, smaller.

Or lab mice. They're already inbred to the point of being clones, so you don't have to worry about genetic issues cropping up in a long term, small colony kept for food.