We have found this website for transfers to and from the Airport for 3 euros
http://www.pafosbuses.com/ booking tel 00357 99370444 info 00357 26934410 please check with them for timetable as there will be less trips in the winter season
If you wish to book the transfer, please at time of booking the transfer state the drop off venue as the Kefalonitis Hotel Apartments on Pyramou Street which is just across the road from the apartment because they do not drop or pick up at private apartments or villas only hotels.
our thanks to Brian and Jill for latest transfer details from the airport:- who used Suntransfers.com on arrival @ 26 Euros and on the way back we used Paphos Union Taxis, email paphosuniontaxi@cytanet.cy (25 Euros) which gave very good service. They are based not far from the apartment on Tomb of the Kings Rd between the Chinese Restaurant and the Irish pub.