Everyone knows the Mama Cass version, and hers is fine, but nothing can ever touch the Ella and Louis recording. The lyrics make it an obvious lullaby, but there's so much more happening here. You can sing it straight up, or you can follow Ella and Louis' phrasing, sing their embellishments and scat parts, hum the trumpet intro and ending. My kids are an unusually receptive audience for my Louis Armstrong voice, probably because it so closely resembles my Cookie Monster voice.
Old jazz standards make great lullabies in general. The lyrics were written in a more innocent time, so you don't have to worry about inappropriate content. The tunes were meant to be sung by regular people around the piano, so even if you don't have Ella's chops, you can still pull them off and feel good about how you sound. And the melodic sophistication and subtle wordplay help to balance out all that old-timey earnestness. Besides, little kids don't know about irony yet, so earnest is the tone you want.
You can learn more about Ella Fitzgerald here
You can learn more about Louis Armstrong here
About the Curator - Ethan Hein
Ethan Hein is a Doctoral Fellow in Music Education at New York University. He teaches music technology, production and education at NYU and Montclair State University. With the NYU Music Experience Design Lab (https://www.musedlab.org), Ethan has taken a leadership role in the creation of new technologies for learning and expression, most notably the Groove Pizza (https://musedlab.org/groovepizza). In collaboration with Soundfly, he has developed a series of online music theory courses (https://soundfly.com/courses/unlocking-the-emotional-power-of-chords). He maintains a widely-followed and influential blog (http://www.ethanhein.com), and has written for various publications, including Slate, Quartz, and NewMusicBox.