You won't find a birth record for him unless you can find his church baptism record.
I'd look for his birth announcement in the local newspaper. I'd first check the Library of Congress, Chronicling America. Then I'd contact the North Carolina Digital Collections, digitialncdcr.gov who has newspapers back to the 1700s. The North Carolina Digital Heritage Center, www.digitalnc.org
also has newspapers.
Do you have a copy of their marriage record? Their parents names might be on it.
If you don't and can't order it, I'd look for their newspaper marriage announcement.
Also look for his newspaper death notice. Successful Searching!