MOST cats can't or won't kill chickens or ducks, but if they're big enough, or starving, they might try and in doing so, injure your poultry. It sounds like they are more after the chicken feed than the chickens. Do you WANT a cat? Trapping them, and taking the ones you don't want to the pound will get them away, and you could feed one and let it live in your coop to keep down mice and such. Just a thought, and I know not everyone likes having them around. My teenage cat tries to stalk my hens, it's pretty entertaining but he'd be hopelessly confused if he ever caught one, plus, they turn around and stalk him too, so I guess they're even. Eventually he gets tired and lays down watching them, and they go back to ignoring him.