Welcome! Thanks for asking your question. My name is***** am a licensed veterinarian and I will be assisting you today. First I need to ask you a few questions so that I can be well informed and give you the best advice.
1- How long has this been going on?
2- Any pre existing medical conditions?
3- Has he been seen by a vet for this problem?
4- How much does he weigh?
I am sorry for the delay in response. I will have an answer for you shortly please give me a few minutes.
Friend, there are many possible causes for a chronic cough in an older dog. It will be difficult for me to determine the exact underlying cause without a hands on examination. But, common causes in small breed older dogs are: A collapsing trachea, this is when the rings around the trachea become weak and collapse the dog will then hack or cough to re-open the trachea lumen. Another common cause is an underlying heart disease, less likely lung disease, etc. to name a few causes.
In this case, I would strongly recommend hands on examination with family vet to listen to his heart and lungs and rule out heart disease. In the meantime you can start him on Robitussin DM (cough) 1/2 teaspoon every 6-8 hours. You can buy Robitussin DM over the counter in any pharmacy (chemist); make sure it is Not sugar free; No phenylephrine.
My goal is to provide you with excellent service - I hope I've provided the information you were seeking, if you feel you have received anything less, please reply back as I am happy to address follow-up questions. Kindly rate me when you are done.