Small farm animals for meat production, which would be the best producers?

Just depends on the type of meat that you want or like. I have tons of friends who keep chickens, just 2-3. They have a little house for them and section off a tiny bit of the yard. They get tons of yummy eggs. If you do not like eggs then it would not be for you. They can make noise from time to time but the neighbors do not care because they get free healthy eggs out of it from time to time.

EDIT: there are very good answers, you just do not like any of them. To be honest I am really not sure what you are looking for. Birds and some species of fish is about as small as you can get for animals that are farmed for food but you do not want them. You also want something that requires little care, no tanks, no ponds, no pens, little to no sound. You have ruled everything out.

EDIT: chickens require little to no maintenance or space unless you plan on having a ton. I am sorry but if you do not think you could handle a couple chickens and that they take too much work then I think you should let the idea go.

I have to agree with The Cheshire's answer and additional comment.

You've systematically elliminated all the reasonable answers. Looks to me you're not ready to make any kind of commitment to raising much more than grubs in a log. <-- which, BTW, are great protein source.

ALL livestock requires containment!

Rabbits would need a hutch, but they multiply so fast you would have a good supply of meat.