C.P.
This might sound like a strange one but pay attention to if it happens around when he eats. Sometimes food sensitivities can cause people to cough especially products with gluten. It can happen with any foods though if he is sensitive to them. A test for that is an IgG blood test but a medical doctor won't think it's worth doing but I know many people whose health has improved after doing that test and cutting out the dietary culprits!