There aren't that many family farms, and they're going to tend to have about as many animals as they can support already, unless there's some reason they don't

There aren't that many family farms, and they're going to tend to have about as many animals as they can support already, unless there's some reason they don't want more (just like any business—otherwise you're wasting capital). You might find some hobbyist-types who have extra capacity and would take a cow or three hoping to sell them later since they're relatively easy to care for if you have fenced land (pigs are a bit more specialized; chickens are already cheap and most probably want the egg-laying kind, not the mutant factory farm meat kind), but that wouldn't go very far.