As Kythera (kappa 2629, and LSJ entry at web address 1) is a second-declension neuter plural, the form should be *kuqhro/qen, which occurs at Homer, Iliad 15.438. The poet Hermesianax of Colophon used (in fr.7, preserved by Athenaeus, Deipnosophists 13.598E [13.71 Kaibel]) *kuqe/rhqen of Philoxenos (phi 393), shortening the second syllable for metrical convenience. The present headword *kuqh/rhqen is unattested outside lexicography.