First, the bad news:
The problem of cheap flights to Cyprus, during winter schedules, has come up before. There are actually very few options open to you.
Since the failure of Cyprus's own budget airline (Ajet), the only scheduled services from the UK to Cyprus are with these operators:
BA (Heathrow to Larnaca) - currently in the middle of an industrial dispute, so I wouldn't recommend booking with them.
GB Airways (Stansted & Manchester to Paphos). This is the budget arm of BA, so it's possible that their cabin crew could be involved in the same industrial dispute. Additionally, Paphos is about 2 hours additional drive from Paralimni. Larnaca is far more convenient.
Cyprus Airways - See below.
Eurocypria. This is the budget arm of Cyprus Airways but their UK flights (from Gatwick, Humberside & Manchester) only operate from May to October.
Several charter companies (including MyTravel) operate to Cyprus but, to the best of my knowledge, there are no winter flights. (MyTravel doesn't have flights until 1st May).
So it looks as if you'll have to travel with Cyprus Airways.
And now the good news!
Trying some sample dates on the Cyprus Airways website (and choosing Tuesdays because that's often the cheapest day to travel), I found that the four of you can travel for a total of CYP646. That's equivalent to
�141.50 per person, including all taxes and charges.
That's flying out from Heathrow, on 27/02, at 0945 (landing at 1610) and returning from Larnaca, on 13/03, at 1745 (landing at 2045).
I've not tried every possible combination of dates, so it's possible that you might even be able to travel slightly cheaper:
http://www.cyprusairways.com/
Chris