In the UK and Western Europe the widespread transition to disposables seems to have happened around the early 80s, and in the East Bloc in the 90s after the end of the Communist system. I was born in Hungary in 1990 (East Bloc, but a relatively developed member of it like East Germany and Czechoslovakia) and I was initially diapered in cloth, but my parents started using disposables for the night when I became a toddler and wet more. My Mom says they were somewhat expensive, but very convenient and kept the bed dry.