Both happy and happen go back to the noun hap, meaning “chance, luck, fortune.”

Happiness happens happenstantially,
for want of a better word, although
coincidentally, or fortuitously would do.

I guess. I suppose. At a push. And a shove.
There are no certainties in this life although
if happiness is anything it’s certainly uncertain.
Or it might be a warm puppy. What do I know?