Final answer:
Merv Griffin composed the lullaby "A Time for Tony" for his son and used it as the theme song for Jeopardy!
Step-by-step explanation:
The TV show for which Merv Griffin used his lullaby "A Time for Tony" as the theme song is Jeopardy!.
Jeopardy! is a popular quiz show that quizzes contestants on a wide range of topics.
Merv Griffin composed the lullaby for his son and decided to use it as the theme song for Jeopardy!, which turned out to be a very successful decision.