I have identified two daughters of this couple. The estate papers of Nanny or Nancy Turner in Person County, NC, 1830-1833, list James and Charles Poyner as heirs. Nanny Turner was unmarried. Her heirs were the descendants of her parents, William and Sarah Turner of neighboring Halifax County. They aren’t specified as such, but a comparison of Nanny’s heirs with those in William Turner’s will (written 1795, in probate 1808) proves who they were. The same estate papers let us identify the wives of John Cloar and Henry Workin, who married Turners (not Bartletts) in Sumner County, Tennessee. I have posted synopses of the will and the estate papers (see messages 19151, 19152 and 19153 in the Turner Genforum). James and Charles Poyner had married Bartlett women in Person County.
Person County, North Carolina Marriage Records, 1792-1868 (at Ancestry.com) James Poyner & Elizabeth Bartlett, 7 September 1815 (Jacob Vanhook, bondsman, Jno. Garner, witness) Charles M. Poyner & Sally Bartlett, 8 May 1816 (William McKissack, bondsman)
Neither James nor Charles was present to receive his legacy. Both, with Cloar and Workin, were among a group of men who had given John Stanfield a power of attorney. I believe all these men were in Tennessee.