Of American-English origin, the colloquial expression Vatican roulette designates the rhythm method of birth control, as permitted by the Roman Catholic Church.

With allusion to the unpredictable efficacy of this contraceptive method, the expression Vatican roulette is from:
– the name Vatican, denoting the authority of the Roman Catholic Church;
– the expression Russian roulette, denoting the practice of loading a bullet into one chamber of a revolver, spinning the cylinder, and then pulling the trigger while pointing the gun at one’s own head.

The earliest occurrences of the expression Vatican roulette that I have found are as follows, in chronological order:

1-: From Speakers Differ On Sex, But Agree On Marriage, published in the Addison County Independent (Middlebury, Vermont) of Friday 13^th December 1957:

Four widely divergent speakers expressed widely divergent views on sex, in the fifth annual Middlebury College Religion Conference last weekend. Stand-points on “The Role of Sex in Life” ranged from the startlingly secular taken by Dr. Ernest van den Haag to the conservative Catholicism of Dr. Jack Curtis, who was still liberal enough to call the church sanctioned rhythm system of birth-control “Vatican roulette.”

2-: From the San Francisco Chronicle (San Francisco, California) of Monday 7^th December 1959:

Pike Talks On Ethics of Birth Control
By William Keller

Birth control by the rhythm system is a kind of “Vatican roulette” in which couples sometimes fail in their duty not to have children, the Right Rev. James A. Pike, Episcopal Bishop of California ¹, said here yesterday.
The bishop gave his views on the rhythm system in a sermon at Grace Cathedral—a sermon, he said, that was the first in the current birth control controversy “based not on the political implications, but on the ethics. . .”
The controversy developed when the National Catholic Welfare Conference, in opposing use of government funds to promote birth controls, reiterated the Catholic position on birth control. The Catholic teaching is that family limitation is permissible in some cases but only by abstaining from intercourse during fertile periods—the rhythm method.
Any use of contraceptives “is wrong and immoral in itself,” the conference said.
In his sermon, Bishop Pike explained the views of his church:
“If a couple conscientiously decide they should not have a child,” he said, “they are under a positive obligation to use the most effective medical methods to prevent conception.
“They should not carelessly and improvidently bring children into the world, trusting in an unknown future or a generous society to care for them. . . .”
If no children are desired, he said, “we are responsible for using the most effective legitimate method for achieving that end. We are not permitted to use a ‘chancy’ method, like the rhythm method—which some have called ‘Vatican roulette’—when a more medically sound approach is available.
“The sexual act expresses the love and commitment the couple already possesses; it also strengthens and inspires that commitment.”
Later in the day, Bishop Pike commented again on the political aspects of the issue. He said voters should “give careful consideration to views of candidates, so by next term we may help nations who request aid in birth control.”
Since President Eisenhower has stated no foreign aid could be used in this way so long as he’s in office, “it’s now up to Congress to give direction to the President in this regard,” the Bishop said.
He said he was “gratified and surprised” by statements by Governor Edmund G. Brown, a Catholic, during the week. Brown said if he were president he would give birth control information to foreign countries if Congress so directed.
“Recent comments by some candidates and others have been entirely off the point,” Bishop Pike said.

¹ James Albert Pike (1913-1969) was the Episcopal Bishop of California from 1958 to 1966.

3-: From Herb Caen’s column ², published in the San Francisco Chronicle (San Francisco, California) of Friday 11^th December 1959:

Mrs. John Campion figures that Bishop James Pike’s crack at the Catholic Church’s stand on birth control—the Bishop called it “Vatican roulette”—is strictly a case of “Pike’s Pique”.

² Herbert Caen (1916-1997) was a U.S. humorist and journalist.

4-: From the account of the third Search for Truth Forum at the University of South Florida, by Virginia Davis, published in The Tampa Times (Tampa, Florida) of Wednesday 29^th November 1961—the Rev. Charles Bolton, a Catholic priest from St. Leo, was quoted as saying:

“Marriage does not mean you have to breed like rabbits and produce a lot of children you don’t want and nobody else wants, and that you can’t care for and educate properly,” he said.
Most couples want children but “do not necessarily require a whole tribe of them,” he said.
He said some misconceptions on birth control views of the church arise even among Roman Catholics and received a round of applause when he said some communicants of the church refer to the rhythm means of birth control as “Vatican roulette.”
“Rhythm is not the answer to the problem. The answer is to use reason,” he declared.

The earliest British-English use of the expression Vatican roulette that I have found is from the review ³ of The British Museum is Falling Down (London: MacGibbon & Kee, 1965), by the British novelist David Lodge (born 1935)—review by Irving Wardle, published in The Observer (London, England) of Sunday 14^th November 1965:

The first chapter of The British Museum is Falling Down had me in a state of helpless giggling and ready to announce the funniest book of the year. Up to page 26 we witness breakfast chaos in the home of Adam Appleby, a Catholic post-graduate student terrified that a fourth child is on the way in spite of strict adherence to the rules of “Vatican Roulette.”

³ The expression Vatican roulette does not occur in the novel itself.