Will agree with Caregiver222.
I would reconsult the physician who prescribed the Coreg and ask him/her about this.
Yes, your doctor can give you a prescription for anything. That is what they are there for, to give advice and to provide you with the medicines that are needed to treat your problems. Otherwise, they will refer you to the relevant nurse etc.
As you probably know these are two names for the same exact same drug, one being the brand-name and the other the generic name. On a prescription a physician has the option of permitting a generic filling or restricting the filling to a brand-name. With the caveat that in the United States some general practicioners will refer you to a specialist before prescribing a drug that is used to treat heart failure there is no reason your physician should not respond favorably to your request.