When maintaining a steady 2000 rpm the carb coughs intermittently. It does not do this when accelerating, only on flat road, and it doesn't do it all the time. Nothing has been done to it lately. Any ideas?

 

Idk, but the bike shouldn't be cruising at 2k rpm, need more info

 

Most likely the slow speed jet in the carb is partially clogged or too small.

 

Probably normal. Mine coughs when it's not warmed up. Or if I'm lugging it. And 2k RPMs means your probably lugging it.

 

If your bike is jetted properly it will not cough through the carb even if it is cold or lugging. Coughing means one thing, it is lean.

 

My 2000 Road King (EFI) does the very same thing. Big bore kit & Power Commander 1 installed when bike was purchased by selling dealer. I find it strange that this ONLY happens while holding a steady speed, and only occasionally. Current mileage is 74,000 miles, and now I pretty much just ignore this. no one can give me any real answer. One dealer thought it was excessive wear on throttle body, that really makes no sence.

 

I believe you already have your answer but the question is what do you do about it? 2000 rpm tells me one of two things - either you're lugging it or you are inadvertently describing a common issue - a partial throttle condition that is often solved by shimming the needle.

Questions:
How long has this happened? Sudden change or been that way?
What exhaust and intake do you have?
Any different jets than stock?
Have you opened up the mix adjusting screw on the carb?

What I'd do:
First check the plugs to see if they show signs of lean. Post a picture here if you can.
Determine how many turns out from lightly set the carb currently is. Adjust based on findings from the plugs.
If needed, dig into the carb to check the diaphragm for holes/tears (a bright flashlight works well), check what jet sizes you have and ensure they are all clean and clear of any buildup.
Shim the needle.

A Sportster likes the 3000+ range and loves the 3500-4500 range. Ride it hard.

 

Insure your air/idle mixture screw is out about 2 1/2-3 turns, and then bump the pilot up a size at a time, until the lean condition is gone.
Scott