I've never gotten constipated from eating bananas. I've eaten up to 18 in a day… I try to eat as many as possible each day. The more brown spots (no green) they are the more sweet they are, and your body will handle them better.
Never eat them with any green on them—that may be what causes constipation. I never eat them, and I've never had a problem, so I wouldn't know for sure if that's what causes it.