Hi Tony, personally I find the whole of Cyprus good for birding, but have a personal preference of the south of the island, as there is a greater amount of sites, which are also less sensitive in terms of political tension. If you search back through threads on Cyprus there's a lot of good info about which sites to visit, the best sites and also where you'd likely encounter migrants. Sites at which birding is prime include Paphos Headland, Mandria, Askepremos Dam, Larnaca Sewage Works and Pools, Aknha Dam and the Akrotiri Peninsula.
During my 3 visits to Cyprus i've only seen one incidence of shooting, and this was at the M1 pools near the Akrotiri Salt Lake. Reading the book it said ''these freshwater pools are superb for herons, egrets, waders, and the surrounding bushes good for passerines'' I remember excitedly arriving on site to see a Turtle Dove come tumbling out of the sky and 3 guys with guns in nearby bushes. Although not that prevalant these days (as far as what you see as a birding tourist), it still goes on and you could run in to it taking place, though I doubt that any one area is worse than another.
HTH