Welcome to History Hub,
I found a family tree that includes a George Washington Ballard born 1824 in Coweta,
familysearch.com is a free website you just need to register to search.
Good Luck in your ancestry hunt.
Dear Mr. Ballard,
Thank you for posting your request on History Hub!
The Federal Government does not ordinarily create or maintain birth, death, marriage or divorce records. Such records are made and kept by State and local governments rather than the National Archives. For a copy of various vital records for George W. Ballard, we suggest that you contact the Georgia Division of Archives and History as well as review the FamilySearch research wiki on Georgia Vital Records.
We hope this is helpful. Best of luck with your family research!