Manning was one of the cardinal electors who participated in the conclaves of August and October 1978, which selected Popes John Paul I and John Paul II respectively. Before entering the August conclave, he noted that the Church "has no political support in many places" and called for a pope who could "change people through warmth." In 1981, John Paul II sent him as a special papal envoy to the celebration in Drogheda, Ireland of the third centennial of Saint Oliver Plunkett's martyrdom. He called for a halt to the deportation of Salvadoran civil war refugees in 1983.