How can I add my father to my birth certificate at the age of 47 without my mothers help. My father has no problem being and did not know he was not on my birth certificate. My mother said she don't want him on it

Before you start the process your mother has no choice in the matter.

Why do you want to do this and where?

Has DNA confirmed paternity?

What state do you live in as some states may not allow it after a period or without bringing it before the courts attention for a ruling.

Also has DNA testing been done?

The key question is why? The only legal reason is to provide for inheritance, but your father can do that by providing for you in his will. On the other hand, he can leave you out of his will and his being on your birth certificate can mean squat.

As noted your mother has no say in the matter.

ANY question on law needs to include your general locale as laws vary by area.