You could maybe try a few chickens.....
I had chickens at my previous house. we had a good sized back garden. I had 7 in total (2 Fenning Black, 2 Mendlesham Blue and 3 ex battery hens) and they were just free to roam around the garden. I made a run from 8 pieces of Heras fencing (two sheets on the bottom, two sheet on the top and one on each side that we put them in if we went out for more that a few hours and at night.
Loved having the fresh eggs and just sitting in the garden watching them get up to their antics!