Monroe and Martha Cox, ages 21 and 16 respectly, are located on the 1850 Cass County census (later Bartow County) GA immediately following two Abernathy households, both headed by a son of Nathan Abernathy & Eve Cline. Daniel was only recently married and couldn't be your Martha's parent, but Isaiah had been married long enough and was old enough to have had a 16 yr old daughter in 1850.
I have information that Isaiah and his wife Mary Faulkner had a daughter Martha who was reported as born 27 Apr 1834 in a post (perhaps in a GenForum message base) citing a Faulkner family Bible in possession of a William Faulkner as of 2001. As I don't have the bible nor a copy, I can't verify that. However, I also can't refute it. And the proximity of Monroe and Martha Cox to the family of Isaiah Abernathy would certainly tend to suggest that Martha was a daughter of Isaiah.
The Old Macedonia Cemetery website http://www.beyondthepalace.com/macedonia/http://www.beyondthepalace.com/macedonia/ cites a number of Cox and Abernathy burials, including a William M Cox, who is noted as being a son of James Monroe Cox and Martha Abernathy.
According to my notes, William Faulkner, who had possession of the Faulkner Family Bible with data, stated that Mary was daughter of Nicholas David Faulkner, b: 29 May 1770 in Cumberland Co., VA., d. 12 Oct 1842 in Lincoln Co., NC andNancy Ann Allen. b: 22 Jan 1779 Lincoln Co., NC and d. 5 Aug 1851 in Lincoln Co., NC. Isaiah and Mary's marriage is recorded in Curtis Bynum's "Marriage Bonds of Tryon and Lincoln Counties, North Carolina", Catawba County Historical Association, Inc Newton, NC (1929), p. 9, bondsman James x Abernathy, and Mary's maiden name is spelled Fortner.
Nathan Abernathy, Isaiah's father, married Eve Cline 28 Jan 1808 in Lincoln Co., NC (Bynum, op cit, p. 10), and apparently was a son of Miles Abernathy and Ursula Bradshaw, who married 6 Oct 1781 in Lincoln Co., NC (Bynum, op cit, p. 10, bondsmen Vincent Cox and John Abernathy). Vincent Cox's wife's maiden name was Abernathy, so there's a strong connection streaching back over the years between the two families.
I suggest that if you haven't, you may want to check out that cemetery website.