Your questions are often very hard to answer, because you're asking about the "correct" way to say something that is either slang or colloquial or extremely casual speech. In this case, there's no correct term for describing a band that's popular with college stoner kids. You can call them a "college stoner band," and everyone will understand you (at least in the US). You can also call them "a college stoner sort of band." You could probably call them a dozen other things that would be equally understandable, like a "stoner-kid band" or just a "stoner band." I honestly have no idea what term I would use if I wanted to describe this kind of band -- it would probably depend on who I was talking to, and whether I was trying to use the description as an insult, or just a neutral observation, or a positive endorsement. I can imagine some native speakers saying either of the phrases you're asking about, but many native speakers, even in America, would never say either one of them. There isn't really a better and a worse option. No matter what you say, it will be a creative attempt to describe something that doesn't have a real name.

But would you say “A college stoner band” or “A college stoner kind of band”?

@Gary: In the US we do still say "stoner." I mean, I don't know if teenagers still use the term, but anyway people my age (mid 30s) and older certainly do.

Neither. Does anyone still say stoner?