Near the end of the “Krusty the Klown Komeback Special” episode we see Liv Tyler looking at her diamond ring and watching the special on TV. Performing on the show is some guy playing a jingle on water-filled glasses.
What song is he playing?
Peter and the Wolf played by Hugh Hefner. (question #94)
Specifically, it’s Peter’s theme (since each character has his own theme)
And that would be Liz Taylor, not Liv Tyler.
Wow, you people amaze me 
But Steven Tyler was on that show.
No, he wasn’t. Steven Tyler (along with the rest of Aerosmith) played at Moe’s Bar when the “Flaming Mo” drink (aka the Flaming Homer) was popular.
The episode described in the OP is “Krusty Gets Kancelled”.
Liv Tyler has never appeared on Simpsons, at least according to her imdb.com filmography.
If memory, serves The Red Hot Chilli Peppers were in this episode.
Flea: We’ll never compromise our music!
Krusty: Uh-huh. But where it says here, “What I got, I want to give it put it in you,” how about we change that to, "What I got, I want give it hug and kiss you?
Flea: Why, that’s much better!
Anthony: Yeah, now it’s a song everyone can enjoy!