A citizen of Cyprus is a Cypriot or a Cypriotess.
Very, very occasionally there are references to Cyprians.
A reminder/word of warning boys and girls ....(and Milti) , that those who follow the example of the Former Colonial Power and the Partitionists, whether through political ambitions or just laziness, and talk of "greek-cypriots" and "turkish-cypriots" are increasing the risk of ending up with very real Greek Cyprus and Turkish Cyprus.
So what's it to be chaps and chapesses? Cypriots or motherland-feckers??
(Doesn't really bother me of course being a sort of Englishman.)