Motorcycle Repair: Carb coughing, dyno jet kit, sportster 1200

Question
QUESTION: I have a '03 FXDWG, with carb. I have paperwork from when new and the original owner had S/E Air Cleaner and S/E II slip-ons installed. Paperwork also shows a new main jet, from XL1200, part #27114-88 and a slow jet, size 48, installed. From the time I have owned it, it has occasionally "coughed" when cruising at steady throttle and sometimes when going through gears. "Coughing" seems to have gotten worse lately. Will the installation of the early Sportster 1200 needle, part #27094-88, stop the cough?

ANSWER: Pull your plugs and let me know what color they are
Mike

---------- FOLLOW-UP ----------

QUESTION: They are a little on the whitish side.

Answer
Since they are while you are running lean, which could  cause the coughing. A couple of other things that can cause your problem is a leaking intake or a leaking intake valve. If it were me I would install a Dyno-jet kit. That will give you the correct jets, needle, and will give you more throttle responce and it will richen the carb back up.
Good luck and happy riding
Mike