The Collaborative International Dictionary of English v.0.48:

Honeyberry \Hon"ey*ber`ry\, n.; pl. -berries.
   The fruit of either of two trees having sweetish berries: (a)
   An Old World hackberry (Celtis australis). (b) In the West
   Indies, the genip (Melicocca bijuga).
   [Webster 1913 Suppl.]