Hmmm, tricky, it's generally not advized to put bettas in with tetras as they can get quite nippy, I'm not sure if this is true for black neons as I've never had them but normal neons can get fin-nippy so they aren't advized, but some people have kept neons with bettas succesfully so I won't rule it out as a possibility, however if you do decide to do it pleasepleaseplease make sure your tank is heavily planted so the betta can get away and hide and watch them VERY carefully so if there is a problem you can remove the betta quickly.
I personally wouldn't advize this or put them together myself, but others have done so with success so it really depends on the fishes temperment.
-Rezz
[Edit: Sorry just realized it was a community and not just other tetras in there, what other fish are there? This could be quite important as tetras aren't the only fish that might go for the betta....]