The Wijngaards Institute for Catholic Research claims to have the original prayer used by the Apostles and their successors for deacon ordination, which begins, "Hear, o Lord, our petition and send down on this your maidservant..." The Institute lists the prayer along with a detailed explanation on its website.
The Catholic Church is not the only faith that ordains deacons. The Episcopal Church has a prescribed service for deacon ordination. It includes a prayer that begins, "O God of unchangeable power and eternal light: Look favorably on your whole Church, that wonderful and sacred mystery..."
As an example for Baptist Churches, the Redland Baptist Church in Maryland has printed a transcript on its site for the ordination service it holds for new deacons as of 2016. In it, a hymn written by Charles Wesley reads much like an ordination prayer and could be used as such. It begins, "A Charge to keep I have, A God to glorify, A never-dying soul to save, And fit it for the sky. To serve the present age, My calling to fulfill..."