Cyprus is in effect two countries since the Turkish invasion. Both don't allow detecting inland for antiquities even if you own the land.
Regarding the beach I would detect in the Turkish sector but would be very wary in the Greek sector.
If you did turn up something old/interesting it would have to be given up and there's a M.O.U. agreement between Cyprus and the States whereby the U.S. customs will demand importation paperwork if they find any Cypriot antiquities/old coins on you or in your luggage.
I think there's still a Whites dealer on the island (Cyprus Metal Detectors). I should look them up on the web and if their site doesn't say anything e-mail and ask what the current situation is.