I had the same problem years ago, rabbits eating the beans as soon as they came up in the garden.
I caught one sitting in the flower bed and made a perfect shot (I thought) with a field pointed arrow. Well, the rabbit took off through the neighborhood looking like a shish kabob.
I could see the news crews filming this horrible case of "animal cruelty", police cars racing to the scene and me being let away in handcuffs to face two life sentences for the heinous crime of putting my green bean crop above some cute, fuzzy animals life.
I ran like a mad man through some of my neighbors yards and finally cornered the rabbit, stomped him to death and quickly retreated back to the safety of my yard.
Moral to this story, use a broadhead.