Not sure if this helps but we used to go to Cyprus quite a lot as a friend had an apartment out there:
Flights are fairly regular with SleazyJet so it's quite possibly cheaper to book these and the accommodation separately. Touching on what Playing with Fire UK said, check the midweek flights. We always found it cheaper to fly out on a certain day and then return on a different day the following week. Eg. fly out Tuesday, come back Thursday or Friday. Of course you will have to have flexible accommodation to do that.
Cyprus is a small island so it's highly likely that airport transfers (especially coach) will be a rip off. We always found it cheaper on other holidays to get a taxi from outside the airport if we weren't hiring a car.
If you do hire a car: Often the policy is that the car is full of petrol when you collect (which you are charged for) and then you are expected to return it empty. So don't make the mistake of filling it up before you drop it off!
June is a good time to go if you like it warm. Cyprus is generally pleasantly warm between March and November in my experience so other months will be cheaper but you're still getting the weather. Last August was ridiculously hot - the traffic lights were melting.
But yeah as you say it generally does cost a bomb. The cheapest way is to not go at all, but if you're meeting all your financial goals why not splurge a small amount?