Later the Greek-speaking Cypriots used a syllabary for writing, long after other Greeks were using the Greek alphabet (and they were in contact with those other Greeks). I guess traditions die hard.
Cyprus (Keftiu) spoke Minoan or a related dialect, Eteocyprian; the Mycenaean Greek speakers took over the former Minoan world, trade routes, etc, and on Crete adapted Linear A (still undecipher) into Linear B.
On Cyprus there’s a short bilingual inscription.
https://bmcr.brynmawr.edu/2015/2015.01.24/
https://www.academia.edu/7174257/The_Amathus_Bilingual_Inscription
https://www.jstor.org/stable/42617368
https://omniglot.com/writing/cypriot.htm
http://www.palaeolexicon.com/Cypriot