Hi, I am Dr. Peter and would like to help.
1- How often is he coughing?
2- Is the cough like hacking?
he coughs only if he moves fast or like more effort is needed such as climbing stairs..
When in his bed or barely moving, he doesn't cough
It sounds like he has an upper respiratory infection. If it is related to a virus his body will get rid of it. If he develops a thick nasal discharge then it is caused by a bacterial infection and will need antibiotics from your vet. In the meantime, for the cough you could give 1 teaspoon of robitussin DM every 6 hours. Follow up with your vet on Monday.
If you have additional questions I will be glad to answer them.