My Virago 250 was running very unevenly, losing power, surging etc. I took out the spark plugs and saw the electrodes were covered in soot. I thoroughly cleaned the plug tips with a wire brush, ran the bike round the block and saw soot build up again. I recleaned the plugs and adjusted the fuel mix screw on the carburettor – which needed to be screwed in a fair amount. I adjusted the screw by screwing in until the bike was just about to cut out on idle then backed off the adjustment screw about ¼ turn. I have run the bike for a week and it was running uneven today. There is some carbon build-up on the plugs, but not as bad as before. I have put new plugs in as they were cheap and will adjust the fuel-air mix again. What do I do if the carbon builds up but the bike is about to cut out when I set the mix to as lean as possible? Could there be some other cause for the carbon buildup on the plugs?
There are other reasons your engine could be running rich, for instance the choke could be stuck partially closed or something else could be constricting the airflow. Your carb float could be out of adjustment as well.
The second cause would be a weak spark, which is possible, but unlikely as it means both your coils would have gone at the same time.
So my money would be on your air intake or carb somewhere, but don't ignore the ignition possibility entirely.