The second option.

I can't imagine ever using the first sentence for the same reason that I would never say "There is trouble" or "There is no trouble". Although those are simple correct sentences, they feel incomplete. You need to locate the "trouble" in space or time. For example, you could say "There is trouble here" or "I smell trouble" or "I feel trouble (coming)" or "This situation is troubling" or "Now we have trouble" You could also say "This (or 'that') is trouble" so long as it is clear to what "this" (or "that") refers. Likewise, if someone said "Don't make trouble when there is no trouble", I would be confused: "Isn't there always trouble somewhere? What trouble are you talking about?" You could easily fix this by saying "bring" instead of "make"; that provides a locality since you can only bring things "here". The second sentence does not suffer from this issue because "where" has the meaning "in a situation in which".

both are correct but they express different meanings

Don't make trouble when there is none.

I think especially your second option "Don't make trouble where the is no trouble/none" sounds just fine. In case you're interested, here are a few other American expressions for the same idea... "Don't stir up trouble." "Let sleeping dogs lie." "Don't poke the bear." (I don't know whether these would sound normal in British English or not.)