You might try to town clerk's office to see if their marriage record lists the parents. The image is not online.
Source: "Georgia, County Marriages, 1785-1950," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:Q2QK-6D4M : 22 December 2016), Moses Peyton and Matilda Brown, 02 Oct 1863; citing Marriage, , Banks, Georgia, United States, county courthouses, Georgia; FHL microfilm 1,597,743.
Name Moses Peyton
Marriage 02 Oct 1863 Banks, Georgia, United States
Spouse Matilda Brown