Hello and thank you for asking your question on just answer. My name isXXXXX will try to help.
Did he just start coughing today?
Does he have nasal drainage and sneezing?
Is he having difficulty breathing?
How much does he weigh?
If he has been coughing on and off for months, he does not have nasal drainage, and he is an older guy, there is a good chance he is coughing because of congestive heart failure. This means the heart is not pumping blood out as well as it used to. Because of this, fluid is leaking into the lungs causing him to cough. This would have to be diagnosed with a chest x-ray. There are medications to pull the fluid out of his lungs and help his heart work more effectively.
If he had a cold, he would have nasal drainage and it would have come on suddenly. That is why the cough medicine you have given him is not working. You can give him up to 20 mg of Dextromethorphan every 6 hours. If you gave him half of a coricidin cold and cough pill you gave him 15 mg which is nearly the maximum allowed amount and it did not help.
It does not sound like a respiratory tract infection or a cold.
I would get him to a vet as soon as possible.
He could also have chronic bronchitis, a mass pushing on his lungs or trachea, or pneumonia. The sooner you can get him to the vet the better.