Motorcycle Repair: 1987 Custom softail miss, intake leak, ohm meter

Question
Mike this is my first harley 87 softail. This bike has been sitting for 4 years. I pulled off the carb and cleaned it out,changed the plugs, wires and oil. This bike only has 13000 miles on it. At low rpm any gear i get a miss that doesnt go away.The dealer says it needs a new carb was looking for your opnion. The dealer says that they are noted for carb problems.
Hope that is enough info.
Thanks  

Answer
First thing I would do is check for an intake leak. Start the bike and let it warm up. Spray a little carb cleaner around the intake. If the RPMs go up then you have a leak. Also, test the coil with a OHM meter. It might be weak
If this doesnt help let me know.
Mike