Answer:
Yes, rabbits can eat runner beans as long as they don't eat too many. Runner beans and other green edible bean pods (like snow peas) are usually fine for rabbits as a small occasional treat (like one small bean pod, or half of a big one, for a normal, healthy 6 pound rabbit).
Beans are generally high in proteins, starches, and/or fats, and these aren't healthy for rabbits. Too many bean pods will make a rabbit sick. Some people recommend avoiding beans entirely and not feeding any to your rabbit because they're just not healthy (including runner beans).
See the related question below for more details and helpful links about a healthy rabbit diet.