You could try Alpha Omega in Kalyves. We used then to sell our property about nine years ago and they were the most professional and energetic of the four agents we placed the property with. A friend also sold their property through them about a month or so ago and formed the same opinion, adding knowledgeable, thorough and friendly.
I'm pretty sure they still deal with property sale and purchase on Akrotiri.
Their website is http://www.aocrete.com
and office telephone is 28250 31860 - Eleni or George Niavridakis are the main people.
From the National Highway either leave at the Kalami junction and follow the road right through Kalyves heading towards Armenoi. As you're getting towards the end of the village there's a petrol station on the right and A-O is about 120m further on the left, with a large, green shop fascia. Alternatively, follow the highway to the next (Armenoi) junction and at the end of the exit road turn left towards Kalyves. As you approach the village there's a large garden centre on the left and O-A is a short distance on the right. This route is longer but you avoid the narrow main road through the centre of Kalyves and possible traffic delays.
P.S. They're multi-ligual, too. (5 or six languages)