I was having similar problems.
The generator would start to hesitate once it got warm, and it would belch out black smoke. I would watch the throttle go to wide open, and it would eventually die, spewing black smoke all the while. (It would actually start to miss, then couldn't recover once it got all loaded up- which I found out later)
Black smoke = rich or not enough air - replaced air filter (needed it anyway) didn't fix the problem.
I replaced the plugs - no different.
I had good spark, fuel delivery was good, and I know there's air.
Checked the gap on the points - small adjustment to .016" but no help.
I fiddled with the idle and main jet adjustments - now it would run, but not right.
I sprayed a can of "4C" in there - fun, but no solution.
I took apart the whole carb and cleaned it out - it was already pretty clean.
I bought a new set of points - problem solved.
When I finally bought the points ($27 w/condenser) the parts guy mentioned "that is probably the most purchased part for your type of generator, they seem to wear out or corrode faster than a lot of the other components".
To which I replied "so I've been in here 3 times in the last 2 days, and you just now mention this?" - we had a good repor going
I thought the points looked fine on initial inspection, but once I had them in my hands compared with the new ones, there was obviously some wear and corrosion.
-Just a tip. The thing runs like a top now.