Hi Tom,
I've visited Cyrpus twice, once in August and once in October/November, and it's one hell of a place to bird, particularly in the time you're going, as far as I know.
The sites I would reccommend are:
Aknha Dam: On the east side of the island this has got to be one of the best places to go. Spur Winged Plover is guaranteed, and theres loads of herons, egrets and waders on the shores of the res. It's also a raptor, pipit and wagtail hotspot, and also good for warblers particularly Great Reed Warbler, I had a White Pelican here.
Askepremos Dam: Really near to Paphos, and a cracking site in the spring. Should yield plenty of crakes and other wildfowl, etc, as well as Little Bittern and the surrounding slopes are good for warblers. The back of the reservoir that this dam holds is also a very good site, there's a small ruined village, and the area around here has lots of falcons, Cream Coloured Courser, Pied Kingfisher, Bonelli's Eagle and Eleonora's Falcons.
Paphos Headland: Another site near to you, a walk round the headland always yields plenty of migrants, as well as good numbers of sea birds etc. Birds such as Richard's Pipits, Izzy Wheatear and Bluethroat are around, so a good area to check for passerines.
Kensington Cliffs: Guaranteed Griffon Vulture and Eleonoras here; also a good site for Cyrpus Warbler.
Phassouri Reedbeds and Akrotiri Salt Lake: Another superb site, the reedbeds here are amazingly good for herons, waders, crakes and the like, and thus attract good numbers of raptors, and the salt lake is a ground roosting hot spot for these. Also on the salt lake is a large flock of flamingos, and a drive round this will take you past Ladies Mile, another wader hotspot.
Larnace Sewage Works: To the east of the island are Larnace Salt Lakes and the nearby sewage works pools, which can be viewed from a hide on stilts. Here there is a spectacular amount of birds, both Audouin's and Slender Billed Gull, White Pelican, waders, wildfowl, Bimaculated and Calandra Lark and all sorts of other bits.
Mandria: The fields near here are superb for pipits, and also a good area to bird in general.
Troodos Mountains: Cyrpus specialities up here, such as the Crossbills, and the tits, but also a good place for Short toed Treecreeper - a bit chilly though, don't wear shorts!
Hope this was all of some use, another good idea is to just wander around areas of unkept land, I found often the best birds were seen where I least expected to see them.
Finally, all of the above sites (with maps) are in a book called 'Birding in Cyrpus' by Arthur Stagg and Graham Hearl, I found this an essential asset whilst on the island, well worth a fiver.
Cheers
Dan