睡覺時咳嗽,但平曰無事, it is probably 鼻敏感, 鼻水倒流 cause咳嗽. You may buy 海鹽水 from 藥房to help him滴鼻 and 聞steam (use 電飯保to create the steam or use 蒸面器). That will make him feel better. If the situation is serious, better send him to see doctor and have pill.
Also keep him always from 毛么仔.