I have looked at some of the records for this area of Georgia, and although I cannot tell you who your Martha's parents were, it is very likely that she was a descendant of Thomas Akins, Sr. of Mecklenburg Co., Virginia, who settled in Wilkes Co., Georgia in 1785. Oglethorpe Co., Georgia, was at one time a part of the territory encompassed within the original boundaries of old Wilkes County, from which Oglethorpe, Warren & Taliferro Counties were formed. The Akins families in these counties are descendants of Thomas Akins Sr.'s sons: Robert, Francis, Joseph, Jacob, and Thomas Akins, Jr. Thomas Akins Sr. also had several daughters, whose married names were: Frances Leggett, "Peggy" [Margaret] Floyd, Nancy Wilder, "Polly" [Mary] Gunnells, "Betsy" [Elizabeth] Gunnells, and Haley Gunnells.
I believe that Thomas Akins Jr. may have died in 1832 in Elbert Co., Georgia, leaving a will, but I do not have a copy of it. Robert Akins won land in Oglethorpe County in the 1805 Georgia Land Lottery, and he had a son named John Akins who died in Warren Co., Georgia in 1814, leaving a will. John's willnamed the children of himself and his wife Winnefred as being: William, John, James, Benjamin, Isabell, Thomas, "Polly" [Mary], Mariah, and Matilda. Of these children, we know that William Akins maried Elizabeth Glen, Benjamin Akins married Elizabeth Holden, Isabell Akins married William Byrom, Polly Akins married Samuel Smith, Mariah Akins married Joseph Jarrell and Matilda Akins married Edmond Harrison. These marriages took place between 1809 and 1831 in Warren and Taliaferro Counties, Georgia.
The key to finding the parents of your Martha Akins would be to carefully examine the court records, newspaper abstracts, bible records, and any other available information which would help you to determine exactly who Martha's parents may have been. Since Martha married in 1826, she was probably born between 1800 and 1810, so you should carefully examine the Akins men who would have had daughters about this age. The 1820 census for Georgia may be of some use to you in that regard, at least as a means of eliminating the men who would not be candidates as her father. She would probably be between 10 and 20 years old in 1820, so try looking at the 1820 census records for Akins households in Wilkes, Warren, Ogelthorpe & Taliaferro Counties, Georgia and see what you come up with. This will at least narrow down the possibilities. Since Martha married a man by the last name of Christopher, pay particularly close attention to any Akins families living in the same county or near any Christopher families, which may be related to your ancestor. This is the best way to find "a needle in a haystack" so to speak.
I hope this may be of some help to you, and I wish you the best of luck in your search.