Hi, well,

lots of possible & interesting causes, the elimination procedure may be the way to go. Btw, which carb is it? Some ideas that comes to mind: Black smoke? then definitely running too rich, not a plug problem. Is it only at low throttle\idle, or do you get a black plug\rough engine on a ride with open throttle as well? Check the plug after a high speed run. Any petrol leaking from float chamber\carb? Check float level & float needle. If you have an airfilter, is it better without it? Jet(s) are correct size?, or are they worn? Needle jet clip at correct position & not worn?
Regards
E.