The 1881 and 1891 Cyprus census as indeed most later ones in Cyprus were simply demographic no names, no addresses simply number of popuilation per village, men -women, Greeks-Turks. Where does one start genealogy research in Cyprus? Local parish (church records) where still available (fotget the north) record weddings, divorces, christenings, burials although older records only record first names e.g. Yiannis tin Maria means that Yiannis married Maria. The date next to the namers helps especially in small villages.School records are useful.
The oldest record available are the Tax Registers from each village 1770(is the oldest) under Turks. All male population paying taxes (14-50 years old).Normally the name and surname with the sum paid e.g Kostis Yiannou 12 piasters.They are kept in the archives of the Cyprus Archbishopric. Old newspapers are helpful (some go back to 1880's)