Not sure what did it but he made up his mind to complain to her about this issue. Only as a hint, of course, because he was too coward to solve the problem up-front.
Is this usage correct? If not, what's a better alternative?
It's acceptable, but it sounds a little funny because you haven't mentioned a specific thing. I can't find the way to express why, but "only as a hint" would sound better if it followed something specific like:
"I mentioned to her that my mother would be visiting, only as a hint".
In your sentence, I think the following are slightly better alternatives:
Only by hinting
Only with hints/a hint
Only by dropping hints (idiomatic, commonly used)
As a side note, I would either say "too cowardly" (adjective) or "too much of a coward". I think this is linguistically correct, but I'm sure plenty of English speakers would phrase it the way you did too.