The Collaborative International Dictionary of English v.0.48:

Clingstone \Cling"stone`\, a.
   Having the flesh attached closely to the stone, as in some
   kinds of peaches. -- n. A fruit, as a peach, whose flesh
   adheres to the stone.
   [1913 Webster]

WordNet (r) 3.0 (2006):

clingstone
    n 1: fruit (especially peach) whose flesh adheres strongly to
         the pit [syn: cling, clingstone]