Cypro-Classical (475 - 323 BC) & Hellenistic (323 - 58 BC):
The Persians occupied Cyprus in about 525BC as part of their 5th Satrapy. Cyprus contributed men and ships to the Persian war against Greece 480-479BC. The Phoenicians in Cyprus, as allies of the Persians gained influence. Kition (a Phoenician colony since at least the 8th Century BC) conquered Idalion around 450 BC. Eventually controlling 6 of the 10 kingdoms, with 3 of the kings being Phoenician. They introduced their deities to Cyprus, many of them corresponding to existing Greek deities (for example Astarte/Aphrodite). However at the start of the 4th century Evagoras took control of most of the island and tried to gain independence from Persia but failed. Cypriots fought for independence several times, aided by the Greeks including a revolt in 350 BC which was crushed by Artaxerxes. Finally Cyprus was liberated by Alexander the Great in 333BC after Cypriot kings supported him in the siege of Tyre.
Cyprus was cut off from trade with Greece till late in the 5th century, after which Greek intellectuals and artist moved between the two countries, influencing Cypriot art, particularly Sculpture which flourished, and jewellery. Large quantities of Greek-style pottery have been found.
The death of Alexander in 323BC marks the start off the Hellenic period. His empire (and Cyprus) was fought over by his followers. 4 Cypriot kings supported Ptolemy I (one of Alexander's generals ruling Egypt) against Antigonos. Ptolomy lost control of Cyprus in 306 and 294 BC but thereafter Ptolomaic Egypt ruled Cyprus through officials in Paphos, abolishing the Cypriot kingdoms. Greek was the dominant language, though the Etocypriot language was still spoken, dying out in the 3rd century. Hellenistic art and culture came to dominate Cyprus and Phoenician and native Cypriot characteristics disappeared, along with the Cypriot syllabic script. Number of new cities were founded. In 58 BC the island was annexed by Rome. Mark Antony gave Cyprus to Cleopatra VII of Egypt and her sister Arsenoe IV, but after his defeat at Actium it became a Roman province again in 30BC, and remained so till the division of the Empire into East and West, Cyprus belonging to East.
Although I have a few coins from Classical I (ie before 400BC), and a couple of other Classical/Hellenic pieces, my collection basically ends with the Archaic period. During the Bronze Age Cypriot art was distinctive. In the Archaic many influences blended to continue a recognisible Cypriot style, but following this Cypriot wares were more and more provincial copies of products of the empires which dominated them. However the history of Cyprus since has been rich and complex and I invite you to find it out for yourself.