Most airlines increase their prices the nearer you get to the departure date and charge the absolute maximum to anyone who wants to travel at the last minute. So you should look directly at the websites of the relevant airlines.
Operators with flights to Larnaca are listed here:
http://en.wikipedia.org/wiki/Larnaca_International_Airport#Airlines_and_destinations
See here for flights to Paphos:
http://en.wikipedia.org/wiki/Larnaca_International_Airport#Airlines_and_destinations
Skyscanner (as recommended above) is a good starting point but it often fails to list the cheapest flights. Budget airlines do their very best to keep their fares off such sites.
Further, if you're thinking of travelling in the near future you'll find your options for flights to Cyprus extremely limited. Most services to Cyprus are 'summer only' and you'll have very little choice at this time of the year.
Chris