I was looking through "Franklin County, Georgia Marriages, December 1805 - 1850" compiled by Matha Walters Acker. Several Paynes were listed. I copied the information for three of them down. These aren't my Paynes but thought I would share the info anyway.

Obadiah Payne and Eliza Ayers married 13 December 1836
C. Addison, J.P.
source: license 1751-03/5-112
see also volume 4, page 7

Thomas Payne and Olive Ayers married 8 November 1829
Samuel T. Payne, J.P.
source: volume 3, page 56

Thomas Payne, Jr. and Mary Ann Adcock married
14 December 1831
Robert Williams, J.P.
source: license 1751-03/5-112
also see volume 3, page 96

If you want a copy of the certificate, you may not be able to get one from the Franklin County Courthouse. You may have to go through the Georgia Department of Archives.

Hope this helps someone!
Katherine