Runner beans aren't toxic. Beans aren't recommended for bunnies in general because they aren't the best for digestion, but your bunny will very probably be alright especially since he didn't eat that much of it. On the bright side, I guess it was a good opportunity to explain to your daughter that she should always check with an adult before feeding something to an animal. The idea that things which are good for us or look like something the animal is usually eating could be harmful isn't always all that clear for children which can end up poisonning their pet with the best intentions (I knew someone whose bunny had been given chocolates, the ones you buy for Christmas... with the nice shiny wrapper which the rabbit ALSO ate, of course - luckily he only had one big stomach ache and survived the ordeal but damn, children always think of things we hadn't foreseen) ^^.
look for signs of his stomach/ intestines getting too large, diarrhea, etc.
