The Flintstones: Season 4, Episode 3

4 - 3: Little Bamm-Bamm

Fred kicks Barney and Betty out of the Flintstones' home and they want a baby badly and wish upon a falling star and the next morning a baby boy is found in a basket on their door step. He was named Bamm Bamm and he turns out to be the strongest baby in the world. Barney and Betty then take steps to legally adopt him. After almost being turned down, they are given the baby.