I can find no evidence whatsoever that Sheen ever took a permissive stand on contraception. He was true to the teachings of the Church on all matters of faith and morals. And if he had ever taken a liberal view of Humanae Vitae, he would be the poster boy for the dissenters. He is not.
Perhaps your friend was referring to an excerpt form Thomas C. Reeves’s book The Life and Times of Fulton J. Sheen, where Sheen was accused of "waffling" on Humanae Vitae during a 1969 David Frost television interview. According to Msgr. George Kelly’s review of that incident, Sheen’s response was simply misunderstood because it was not clearly articulated (see Kelly’s review at www.catholic.net).
Further proof of his fidelity to Church teaching on contraception is evidenced by the following excerpt from his book Three to Get Married:
Planned unparenthood is the deliberate and willful decision on the part of a husband and wife to exclude from God the opportunity to create another to his image and likeness. It is the human will freely frustrating divine will, as certain agricultural policies deliberately control the productivity of the earth for the sake of a higher economic price. The nonserviam of Lucifer has had its catastrophic effect throughout creation, and particularly in those who say: "I refuse to accept from God that which is his holy will, the increase and multiplication of life." The refusing to be a co-operator with God is to spoil and maim oneself, for of the unused talents, our Lord said: "Take the talent away."