The earlier Peanuts animated specials had marvelous jazz soundtracks by Vince Guaraldi (and later others, after Vince's passing). Not sure if jazz trio is the most obvious music to accompany cartoons, but somehow this music blended exquisitely with the characters.

Indeed from what I've read, the network was originally skeptical that jazz trio made any sense in a children's animated show, but it was remarkably successful. A couple of other tunes from the show, "Skating" and "Christmas time is here" are recognizable jazz standards to this day.