Sweet Cypriot dessert wine with a long history, made from sun-dried grapes.
This is exactly the sort of thing I like bringing back from Cyprus: small enough to fit in a bag, but specific enough to remind you where you bought it. Look for a boxed version with a decent date on it, especially if you are buying it near the start of the trip rather than at the airport. It is also the kind of thing you can talk about when someone asks what you brought back, because there is usually a little story attached to where you found it.
Carob syrup is worth adding because it feels like something you actually noticed while travelling through Cyprus, rather than a generic souvenir. The best version is usually the sealed jar, tin or packet from a normal supermarket, spice stall or food hall, not the most expensive tourist version. The ideal version is modestly priced, not too bulky, and good enough that you would buy it again even without the holiday memory.
Firm brined cheese that grills without melting; famous Cypriot export.