Carnley was consecrated a bishop on 26 May 1981 at St George's Cathedral, Perth and installed there as Archbishop of Perth and Metropolitan of Western Australia in the same service. In the 1980s he supported the ordination of women and, on 7 March 1992, he ordained the first women priests in the Anglican Church of Australia at St George's Cathedral, Perth. His sermon on the occasion took as its reference an autobiographical piece by Charlotte Perkins Gilman entitled The Yellow Wallpaper. Carnley used Gilman's account of the self-destruction consequent on a "benignly prescribed, submissive, middle-class role" demanded of women in the 19th century to consider the "implications of the philosophy that women should "stay in their place, maintaining silence, concealing problems and repressing creativity". The yellow wallpaper of the title is what the imprisoned protagonist in Gilman's story peels off the walls as she goes mad. Carnley used it as a metaphor for the situation of the women who had been waiting to be allowed to become priests, saying: "Today, we are peeling away the sickly yellow, faded, silverfish-ridden wallpaper with which the church has surrounded itself and imprisoned women for centuries past in its benign and perhaps well-meaning determination to confine them by role."
In The structure of resurrection belief Carnley outlines several different ways Christians frame their belief in the resurrection of Christ and the way the resurrection frames their faith. He explores notions of the resurrection as an historical event, as an eschatological event and as a non-event. He also explores the role of memory, presence and faith in believing in the resurrection. When Carnley became the Australian primate, his views caused controversy with some, especially in the conservative Diocese of Sydney, where Archbishop Harry Goodhew accused Carnley of breaching church doctrine and betraying the church's belief in the significance of the resurrection and of Jesus Christ himself. Others, including Phillip Jensen, Rector of St Matthias, Centennial Park in Sydney, objected to comments about how the Christian belief in the uniqueness of Christ had been misused to persecute people of other faiths. Some church leaders, especially within the Diocese of Sydney, called for a boycott of Carnley's installation as Primate, but Archbishop Goodhew rejected such calls, which he said would be tantamount to severing relations with the rest of the church. Carnley says he believes in the uniqueness of Christ: "I think Jesus Christ is the way, the truth and the life, but that doesn't mean that other religions don't have any truth at all." He also says he has an Easter faith in the real presence of the living Jesus: "The Christian story, which pre-eminently transmits and celebrates the memory of Jesus and God’s revelatory deed in and through his life and death, should lead us beyond itself to a living encounter with the real presence of all that it celebrates and rehearses: him, whom by story we recall, we actually know as the living Spirit of the fellowship of faith." He also asserted that the resurrection is "the miracle of the Christian tradition".
Books
The structure of resurrection belief Oxford, : Clarendon Press
The yellow wallpaper and other sermons Sydney, NSW: HarperCollins
Reflections in glass: trends and tensions in the contemporary Anglican Church Pymble, NSW: HarperCollins
and a contributor to:
Lost in translation? Anglicans, controversy and the Bible: perspectives from the Doctrine Commission of the Anglican Church of Australia edited by Scott Cowdell & Muriel Porter, Thornbury, : Desbooks
A Kind of Retirement, More Sermons from Archbishop Peter Carnley, Morning Star Publishing, Melbourne, 2016.
Resurrection in Retrospect: A Critical Examination of the Theology of N. T. Wright, Cascade Books, Wipf and Stock, Eugene OR, 2019
The Reconstruction of Resurrection Belief, Cascade Books, Wipf and Stock, Eugene OR, 2019
