S.K.
I would have the Dr. check him out. It could be allergies and the drainage may be running down the back of his throat making him cough. Our 6 yo son has allergies and that's what happens to him every spring and fall. We use a prescription nasal spray (the other meds make him a grouch) and it stops the drainage and the coughing stops.
It could also be bronchitis or a touch of pnemonia. My twins had a persisitent cough last spring and it turned out one had a touch of bronchitis and the other had pnemonia. I had no idea because they were only coughing at night and occasionally during the day.
I would have him checked out to be on the safe side.