Pet Experts of this site are not permitted to give specific dosing directions to a pet they have not examined. Why?
If your pet's cough is due to an infectious cause or even haert-related cause, and we give you the okay and dose to give prednisone, which can cause fluid retention and exacerbate infection by suppressing the immune system, we have just killed your pet.
It is very important you get him into a vet for at least an evaluation, and possible chest x-rays, so it can be determined what the underlying cause of the cough may be.
Absolutely, I would not recommend prednisone at this time.