I first looked into his story when I ended up with a rosary with his face and name on it. He is known as "the rosary priest" and founded the Family Rosary Crusade. Believe it or not, he coined the phrase "the family who prays together stays together."
His cause was opened in 2001, and so we can pray for his intercession and canonization.
Dear Jesus, Father Peyton devoted his priestly life to strengthening the families of the world by calling them to pray together every day, especially the Rosary. His message is as important for us now as it was during his life on earth. We beg you, therefore, to hasten the day of his beatification so that your faithful people everywhere will remember his message that the family that prays together stays together, will imitate him in his devotion to your Mother and ours, and will be inspired by his holy life to draw ever closer to you with childlike confidence and love. Amen.UPDATE:
The Vice Postulator of his cause is Fr. George Lucas, CSC. This is not the same George Lucas who was just appointed Archbishop of Omaha. Neat.