Joannec,
The best time of year for raptors is usually September, with Akrotiri being the best place to go.
For other species, April is regularly the best month to bird in Cyprus, as that's the month every year that the most species are reported. March is a close second. They're mostly migrants (obviously), and mostly passerines. You might also see the heron and sandpiper species that pass through at that time.
For where to go to see all these species, I'm not quite as familiar with the Paphos district. I usually go to Cape Greco, Paralimni, the outskirts of Larnaca, and Akrotiri. From reports of others though (for locations near Paphos), some good spots are near Mandria fields, the Armou Hills, Asprokremmos Dam and nearby pools, and Paphos lighthouse and headland.
Hope that helps.