Is there a better or stronger alternative to Paracodin that may help
him? I hate to see him hacking as I know it hurts and I think now he
needs stronger medication.

A cough can mean significant health issues, or it could mean - a cough.You
have a geriatric dog. In a dog this age, a chronic cough is very likely due
to cardiac problems. Get to a vet and have a full exam with labs done. Don't
self prescribe.

-Sharontoo