Born in Chicago, Illinois, William Cousins studied at Archbishop Quigley Preparatory Seminary Our Lady of the Lake Seminary, and was ordained to the priesthood on April 23, 1927. He then served as director of diocesan missions, and hosted retreats and other services in various states.
On December 17, 1948, he was appointed Auxiliary Bishop of Chicago and Titular Bishop of Forma by Pope Pius XII. Cousins received his episcopal consecration on March 7, 1949 from Samuel Cardinal Stritch, with Bishops John Boylan and Albert Zuroweste serving as co-consecrators. He was later named Bishop of Peoria on May 21, 1952; during his tenure, he established five new parishes and six new grade schools.
Cousins was appointed the eighth Archbishop of Milwaukee, Wisconsin on December 18, 1958. From 1962 to 1965, he attended the Second Vatican Council, during which he sat on the Commission on Communications Media and on the Lay Apostolate. During the civil rights movement, Cousins was pressured to respond to the activities of his priests, particularly Fr. James Groppi, who led many civil rights marches and protests. In 1967, in response to many Milkwaukee Catholics' dissatisfaction with Groppi, the Archbishop stated his support for open housing and Groppi's other objectives but rejected the priest's tactics.
He retired as Archbishop on September 17, 1977, after nineteen years of service. He died in Milwaukee, at age 86 on September 14, 1988.