Prayer for the Eastern Orthodox

O Immaculate Virgin Mary, we your servants, and sons of the Holy Roman Catholic Church, full of confidence in your powerful protection, humbly ask that you would implore of the Holy Ghost, by the honor and glory of His eternal procession from the Father and the Son, the abundance of His gifts for our brethren of the Eastern Orthodox Church, that, enlightened by His vivifying grace, they may re-enter into the bosom of the Catholic Church, under the infallible guidance of her supreme pastor and teacher the Sovereign Roman Pontiff; and thus, sincerely re-united to us by the indissoluble bonds of the same faith and the same charity, they may, with us, glorify , by the practice of good works, the most august Trinity, and at the same time honour thee, O Virgin Theotokos, full of grace, now and through all ages. Amen.
(conclude with three Hail Marys)

This is my slightly modified version of the obviously pre-Vatican II prayer found in The Raccolta by Ambrose St. John, 1877. Here's the original "Prayer for the Conversion of the Greek Schismatics":

O Immaculate Virgin Mary, we thy servants, and sons of the Holy Roman Catholic Church, full of confidence in thy powerful protection, humbly beseech thee that thou wouldst deign to implore of the Holy Ghost, by the honour and glory of His eternal procession from the Father and the Son, the abundance of His gifts for our seperated brethren, the Greek schismatics, that, enlightened by His vivifying grace, they may re-enter into the bosom of the Catholic Church, under the infallible guidance of her supreme pastor and teacher the Sovereign Roman Pontiff; and thus, sincerely re-united to us by the indissoluble bonds of the same faith and the same charity, they may, with us, glorify , by the practice of good works, the most august Trinity, and at the same time honour thee, O Virgin Mother of God, full of grace, now and through all ages. Amen. (conclude with Ave Maria thrice)