I've used these guys for a while in Limassol, but is like a portal to lots of companies all over Cyprus (ie. you book it completely on their website, and then it emails you a voucher for a specific car rental company in the area you booked):
http://www.economycarrentals.com/
Main thing I've noticed is that booking through the above site is a fair bit cheaper than going directly to the company you get linked to. One time it was a good 25% cheaper than the car hire companies actual website (Platinum car hire).
Cheers