Archdale King appears to be at least one source for the claim that the Greek clergy for the papal liturgy ordinarily came from the Monastery at Grottaferata in the past, but I see that the Greek Deacon at the coronation of St. Pius X in 1903 was "Don Giorgio Xenopolis of Athens" who seems to have left no other trace on the internet so far besides that service, though perhaps someone who could search in greek or with greek forms of his name would have better luck.
The Latin subdeacon at the old Papal Mass was an auditor of the Roman Rota and the Latin Deacon of the Gospel was one of the Cardinal Deacons (2 Cardinal Deacons were Deacons of Honor as is still done today), so it's not unreasonable to think that a dignitary might be occasionally selected to take the role, even though this would seem to go against accepted Eastern practice. (It would be interesting to know what the practice was at Constantinople, but I don't even know where to start looking.)
The Office of Papal Liturgical Celebrations doesn't provide any more information. The booklet for last Sunday just says "Il Diacono greco"
The list of all the info on the papal liturgical celebrations is here:http://www.vatican.va/news_services/liturgy/calendar/ns_liturgy_calendar_en.html
Interestingly, next Sunday will be the third Sunday in a row with the Greek Gospel, which can't have happened very frequently. The opening and closing Masses of the Special Assembly for the Middle East of the Synod of Bishops with last Sunday's canonization Masses in the middle.