James D. G. Dunn usually gets the credit for labeling this movement in NT studies. His 1983 paper “The New Perspective on Paul” (Bulletin of the John Rylands University Library of Manchester Manchester 65 (2): 95–122) is cited by Wikipedia as the origin of the phrase, which is used to describe ways of looking at Paul that go back to Krister Stendahl’s 1963 “Paul and the Introspective Conscience of the West” and E. P. Sanders’ Paul and Palestinian Judaism.
But thanks to Logos, I have been reading N. T. Wright’s 1978 essay “The Paul of History and the Apostle of Faith, originally a Tyndale New Testament Lecture delivered at Tyndale House, Cambridge, on 4 July 1978 and then published in Tyndale Bulletin 29 (1978): 61–88. In it, Wright says:
I want now to [offer] a new way of looking at Paul which provides, I believe, not only an advance in the debate between Stendahl and Käsemann, but also a new perspective on other related Pauline problems.
What follows is, in nuce, the same basic position that Wright has now argued at greater length —and with greater depth, maturity, and exegetical richness — in 2013’s PFG.
It certainly appears as though Wright coined the phrase, or at least most of it (not, perhaps, the “…on Paul”) 3 or 4 years before Dunn.