Spyrou, Constantinou, Adamou, Kyriakou, Pavlou, Ioannou,Christou, Antoniou, Demitriou, Markou, Charalambou, Stylianou, Georgiou, Usually anything ending with -OU.
Some less common surnames are:
Magnitis, Koumettou, Procopiou, Timotheou, Moisis, Evagora, Agathocleous, Economou and some others.
To wrap it all up, most cypriot surnames end with -OU, -IS, -I or -A