You could take pot luck and just get a taxi at the airport - agreeing a price first, of course.

If I were you I'd pre-book, we picked one up from the airport last year and it went into Larnaca, the driver then told us he had to take/collect his daughter from dancing or something like that and his cousin/nephew would take us to the hotel. It was not a licenced cab just a car, a bit frightening.......Won't be doing that again....