Other dictionaries see happenstance as meaning more a single chance event producing an effect with coincidence meaning two or more events (not necessarily the same event) happening in the same time and place to produce the effect. Now I think about it I recall some discussion on coincidence in a juristic sense involving bricks fallling from building sites.

I find £5 on the street - happenstance.

You drop £5 just as a bus passes which blows the £5 note across the street where I am passing = coincidence.

Ed Balls turns up and turns out to be Ed Balls and Yvette Cooper claims our £5, enemy action.