Martha's husband was Eli Henderson Byrd II. Together they had at least ten children and eventually ended up moving from Alabama to Indiana during the latter half of the Civil War. One of their children was John Franklin Byrd, and John's daughter was Frances Anna Byrd (my mother's maternal grandmother).
But back to the question of her age and this early date on the headstone. "March" sounds correct as the birth month since this is mentioned on the 1900 census, although the year is still erroneously recorded as 1839. According to the U.S. and International Marriage Records database, Martha's father and mother, George and Elizabeth, were wedded in the year 1827. And that date seems to confirm all the birth years suggested above from the 1850 census.
By May 1910, we find Martha once again widowed and now living with her youngest son Sam Byrd and his wife Lydia. She was bearing her second husband's last name and still unsure of her age, it seems.