"the quince tree or its fruit," mid-14c., plural (construed as singular) of quoyn, coin (early 14c.), from Old French cooin (Modern French coing), from Vulgar Latin *codoneum, from Latin cotoneum mālum "quince fruit," probably a variant of cydonium malum (or a separate borrowing from the same source) from Greek kydōnion malon, which is traditionally "apple of Kydōnia" (modern Khania), a famous ancient seaport city on the north coast of Crete.
But Beekes says it is from "an older Anatolian word" and that connection with Kydōnia is Greek folk etymology. He also notes there was a Kytōnion on the Lydian border.
The plant is native to Persia, Anatolia, and Greece; the Greeks supposedly imported grafts for their native plants from a superior strain in Crete, hence the name. Kodu- also was the Lydian name for the fruit. Italian cotogno, German Quitte, etc. all are ultimately from the Greek word.
The quince has suffered a sad fall from favour in Britain. In medieval and Renaissance times it was in high popularity .... Perhaps it is the fruit's frequent intractable hardness, needing long cooking to overcome, which has led impatient British cooks to forsake it, despite its unrivalled perfume. [John Ayto, "Diner's Dictionary"]