See quotation 1705.
1705. The best sort of these cling to the Stone, and will not come off clear, which they call Plum-Nectarines, and Plum-Peaches, or Cling-Stones.Beverley, Virginia, iv. 78.
1837. They [the grapes of the Ovino] taste much like a clingstone Peach.John L. Williams, The Territory of Florida, p. 98 (N.Y.).
1840. The firm-fleshed or clingstone peaches are preferred in America.Penny Cycl. (N.E.D.)