Murphy was named Coadjutor Bishop of Erie, Pennsylvania, on 20 November 1978; he was only the third U.S. appointment of the newly elected Pope John Paul II. He was formally installed as Bishop Alfred Watson's coadjutor, or designated successor, on the following 27 December. Murphy soon visited every parish in the diocese and reorganized the diocesan administration to improve pastoral service to Catholics, delegating some of the bishop's authority and allowing more participation of religious and laity. His 1980 pastoral letter on marriage served as the basis for the diocesan policy on marriage preparation. Murphy was called to the Vatican that same year for a series of meetings with John Paul II to discuss American Catholic seminaries, having spent most of his priesthood as teacher and rector at St. Mary's Seminary. Besides regrouping diocesan offices, he created four vicariates in 1981.
Bishop of Erie
Upon Bishop Watson's retirement, Murphy succeeded him as the eighth Bishop of Erie on 16 July 1982. He founded the , an annual convocation of diocesan clergy for their continuing education and spiritual formation, in 1983. In 1984, he announced a three-year plan to raise $9 million to cover diocesan expenses, including educational and social needs and the renovation of St. Peter Cathedral; the appeal raised over $14 million in pledges. In 1985, he launched a spiritual growth process called RENEW, which attracted the participation of more than 20,000 people throughout the diocese and lasted until 1988. A promoter of the consistent life ethic, Murphy opposed both abortion and the death penalty. He wrote an open letter to Pennsylvania GovernorDick Thornburgh in 1986 voicing his opposition to the death penalty, saying, "We are disappointed, frightened, angered even to the point of vengeance when the lives of others become so warped and twisted that they have become destructive of life itself. We wonder why the gift of life was given to them. But the gift is not ours. Neither is it ours to say, 'They do not deserve to live!'" In a 1989 Christmas message, he declared, "As a means to the peace which He promises us and indeed has made possible for us, may the Prince of Peace gift all of us and our nation with a real awareness of the sacredness of all human life, unborn no less than born." He established and the Diocesan Committee on Human Sexuality in 1987 and, upon the advice of pastors, principals and parish leaders, he merged several parishes and closed one school in 1989.
Handling of Sex Abuse
In a grand jury report released by Pennsylvania Attorney General Josh Shapiro, Murphy was criticized allowing "predator priest" Chester Gawronski to remain in the Erie Diocese after he received reports that Gawronski was sexually abusing children. Both Murphy and his successor Donald Trautman often reassigned Gawronski to different parishes between 1987 and 2002. An allegation of sexual abuse against Erie priest William Presley, who was transferred to the Harrisburg Diocese in 1986, had also been reported to the Diocese by his male accuser in 1982, 1987, and 2002.
Approaching the mandatory retirement age of 75, Murphy resigned as Bishop on 2 June 1990, after an eight-year-long tenure. He spent his 16 years of retirement at in Erie. He later died at the infirmary of the in Erie, aged 91.