The obvious solution would be to have the Romans maintain and expand their foothold in Southern Italy, creating a hybrid Greek and Sicilian culture. If you want them independent, then Rome would have to collapse somehow and a successor state arises.
Of course, with Rome right on the papal doorstep there may not be a schism, at least for not quite a bit longer than OTL. But this area would follow Greek rites and traditions, so it's fair to call them Orthodox.