Try this http://www.pancoaches.com/ the offer very attractive prices,we used them last time we visited cyprus and have no problems

You might want to check these out. I am sure this will be of help:
www.shuttledirect.com/en/airport/LCA/
www.salamistaxi.com/
www.cyprustaxiservices.com/

Internet is the way presented in earlier posts that also exhibits proper links that locates the taxi providers on the said location and it is very difficult and sometimes risky to ask about the taxi because the lack of knowledge about fairs will provide others the opportunity to exploit you, therefore a prior knowledge will provide a hurdle to any person by making you a somehow local person.