All of my information concerning this group comes from the 1987 book The Cross on the Sword by Peter Bander van Duren, a Roman Catholic writer on chivalry.
According to van Duren, this order was founded in 1972 by Archbishop Makarios III, then both president of Cyprus and Ethnarch of the Orthodox Church there. The office of Grand Master is always held by the Orthodox Archbishop of Cyprus. The Order is domiciled in St. Barnabas' Monastery, Famagousta; this is apparently still true even though the monastery is now on the Turkish side of the island's partition line. Only Orthodox Christians may be members of the Order, but others may receive a "badge of religion" for their services.
Cyprus and Famagousta are closely associated in history with the Knights of St. John, and the present-day Hospitallers of Cyprus use terminology and symbols clearly taken from the mediaeval order. However, if van Duren is to be believed, they do not claim to be a direct continuation of the Crusader Order. Because of this, they seem to have avoided some of the difficulties placed in the way of other Orthodox Hospitaller groups.