I wanted to know if I would be able to take my child's father's name off the birth certificate without his consent since we were not married. I didn't want his name on the birth certificate so how can I take it off. He is not in my child's life.

No you can't take it off without his consent.
You can take him to court for child support

Without an adoption, you can't take it off WITH his consent.

No you can't take it off, and as noted you can't even take it off with consent.

If he is not the bio father and you prove it by DNA test it may be possible. ** of course this is not the case.

So he is not in the child's life, that is not uncommon at all sadly.

Have you filed for custody, and have a child support order in place.