This song got no particular name. They didn't actually write a song for the episode. Voice actor for J'onn J'onzz, Carl Lumbly, came up with what Martian lullaby sounds like.
By the quote from Bruce Timm (emphasis mine),
“Sure it borders on being a little too sugary in places; certainly we knew that J’onn singing in the episode would be too much. We were certainly nervous about it and, at worse, we’d be the Star Wars Holiday Special, but when we recorded the episode Carl Lumbly just improvised that Martian song at the end. We didn’t want to write out a song for him to do, because we felt it should have an alien feel. About a week or two before we recorded the episode, he came up with what he felt a Martian lullaby would sound like (courtesy of RetroVision CD-ROM Magazine).”