I'd be pretty leery about putting any poison anywhere near my food source (garden/chickens/etc). I'm going with mechanical or water/drowning traps if it comes down to that.
I've also discovered the truism that my chicken-owning friends have told me - if you get chickens, you're getting mice too.
What I've done since noticing droppings in my hanging feeder is to put a cover on the feeder. After the mice completed ignored the cover and slipped in anyway, I placed a...