Chickens

Livestock upgrade parts can be got as a reward for doing errands for the Townies in Henford on Bagley, the grocery cart owner, the gardening cart owners, the pub owner, the delivery guy and the mayor and the creature keeper etc all have errands you can do for them, (there's an 'help with errands' option when you're talking to them) some of them have livestock upgrade parts as rewards. Also if you're sim has level 10 in handiness they can upgrade the coop and barn without needing the upgrade parts to do it 🙂