Green’s Dictionary of Slang

the notoriously undependable rhythm method of contraception.

1960		N.Y. Times 15 Mar. 79: The only awkward moments were created by Mr. Blanchard. During a discussion of birth control and rhythm he contributed a remark about ‘Vatican roulette’ that was as uncharitable as it was unoriginal.
1965		D. Lodge British Museum is Falling Down 172: That’s another thing against the safe method there are so many things that can affect ovulation [...] No wonder they called it Vatican Roulette.
1979		Maledicta III:2 173: Vatican Roulette n Rhythm birth control method.
1989		J. Morton Lowspeak.
1999		D. Lypchuk ‘A dirty little story’ in eye mag. 8 July 🌐 She told him she had bought a brand-new catcher’s mitt and there was no need to play Vatican roulette. She went in the bathroom, put on her shower cap and came back.