The Laughing Vulcan and His Dog

From Memory Alpha, the free Star Trek reference.

"The Laughing Vulcan and His Dog" is a piece of popular children's music, of the latter half of the 24th century, known to schoolchildren aboard the USS Enterprise-D.

When Captain Jean-Luc Picard and three children were climbing an Enterprise-D turbolift shaft when the ship had been deemed powerless in 2368, Picard suggested they sing a song to get their minds off of their predicament. Marissa Flores suggested they sing "The Laughing Vulcan and His Dog", but Picard, unfamiliar with this song, suggested "Frère Jacques" instead. (TNG: "Disaster")

The song title could be a reference to Sybok and J'onn from Star Trek V: The Final Frontier.