Coughing can be a symptom of allergies, so I'd investigate that--either food or environmental. Maybe keep a diary of what he eats and comes in contact with, to see if you see a pattern.
I would also run a humidifier in the rooms he is in.
I know that cough medicines have been pretty much ruled out for kids your son's age, but my family swears by a natural cough medicine called "Olbas". It has honey and herbs in it--nothing that would harm a little one. We love it! You can find it at coops and natural food stores.