I was looking at a map of the kingdoms of ancient Cyprus where each kingdom was presented to have had either Greek majority , Phoenician majority or was mixed Greek/Eteocypriot so I was wondering if I can find any source that provides more details on this. In this link you can see a wikipedia article listing the kingdoms in Cyprus and their respective reigning ethnicities/majorities(?).
A lot depends on the time-scale you are asking about. Evidence is spotty the further back you go. Many different populations settled or conquered Cyprus over the centuries.
According to the Wikipedia article "Ancient history of Cyprus", Mycenaean settlers arrived in the twelfth century BCE and Assyrian conquest took place by about 700 BCE. The ten city-kingdoms documented c. 673 were primarily Greek, with the exceptions of Kition (Greco-Phoenician) and Amathus (Greco-Eteocypriot). This was followed by a brief Egyptian conquest, then Persian rule up until the Hellenistic conquest by Alexander the Great. Cyprus became a Roman province in 58 BCE.
So clearly the story will be very complicated if you want to cover all of Cyrpus over all that time. If you would like more detail about the late prehistoric period 6th-4th centuries BCE in particular, here is an article that looks worth tracking down.