This prayer is from Father Chad Ripperger:

Lord Jesus Christ, by entrusting to St. Peter and his successors the keys of the Kingdom of Heaven, thou didst establish the office of the papacy. Grant to thy Church, we beseech thee, a pope who, in his dedication to the Sacred Tradition of the Church, will seek to govern the Church according to the Deposit of Faith and for the salvation of souls.

Immaculate Mary, Mother of the Church and queen of Confessors, we consecrate to thee the conclave and the election of the Holy Father. Blessed Mother, look not upon our sinfulness or upon the infidelity of many Catholics who do not accept the teaching of thy Son, but upon the Church which is the spotless Bride of thy son, so that we do not get the leader we deserve, but a Holy Father who will guide the church for the glory and honor of thy Son. Amen.