Hello and hope you are doing well.
His cough could be due to Bronchiolitis, which can cause bronchial spasm and repeated coughing, more so in the night. For therapy bronchodilators are given as syrups or inhalers. Please discuss this with your doctor am sure he will provide further assistance.
Hope this helped and do keep us posted.
Your best bet is to ask this question of either his pediatrician or your pharmacist. Pharmacists are great resources about knowing what is safe to give to children or adults - and they typically are easier to get ahold of than the pediatrician's office!
I hope your little one feels better soon!