Somehow I think this was actually later, with Leno, but I can't find any evidence of it ever happening with either Carson or Leno.
Robin Williams and Harry Connick Jr together, and they literally stole the show.
Williams did his usual crazed thing, but not only did Connick egg him on, Connick kept up with Williams every step of the way.
It's a definite memory, and it was in the early or possibly mid-90s at the LATEST, because I can picture who I watched it with and where we lived. But nothing, not the tv.com site nor imdb, says they were ever guests on ANY show together. I never watched O'Brian, and rarely watched Letterman, but I'm absolutely sure it was Tonight with one or the other.
steve in StL