In the planned music video for "Rhinestone Eyes" by Gorillaz, there's a sequence where Crazy Cyborg Noodle goes on a killing rampage while wearing a creepy ear-to-ear grin, which ends with a close up of her crying eye.
The main character of the music video for "Everybody's Fool" by Evanescence.
Morrissey (in his solo career after The Smiths) has "When I Last Spoke To Carol" where she said:
I've hammered a smile across this pasty face of mine
since the day I was born in 1975.
Everclear's "Wonderful" hints at this.
The song "Ah, but Underneath" from Follies. The entire song sings about a woman who seemed to be something on the surface, but was something different underneath the top layer. But that layer, too, was "just a shell," and so it continues. The very last line is "Sometimes when the wrappings fall, there's nothing underneath at all!" making this a type B.
The chorus of Taylor Swift's "Tied Together With A Smile" is about a Type 1 childhood friend of Taylor's who had anorexia.
And no one knows
That you cry, but you don't tell anyone
Might not be the golden one
And you're tied together with a smile
But you're comin' undone
"Smiling Faces", sung by The Temptations, the Undisputed Truth, David Ruffin solo...
Smiling faces sometimes
Pretend to be your friend
Smiling faces show no traces
Of the evil that lurks within...
"The Places You Have Come To Fear The Most" by Dashboard Confessional is about a Type A:
Buried deep as you can dig inside yourself, hidden in the public eye
such a stellar monument to loneliness.
Laced with brilliant smiles and shining eyes,
perfect makeup, but you're barely scraping by.
Lady Gaga's "Dance in the Dark": "Baby loves to dance in the dark / cuz when he's looking she falls apart".
"So Happy I Could Die": "I do my hair / I gloss my eyes / I touch myself all through the night."
Skin's "Nothing But" rings as either a type A or B. The entirety of the song has lyrics which insist that the narrator is happy ("I feel nothing just joy, and pride, and happiness.") but the tune denotes a sense of Lyrical Dissonance.
The song "GIFT of Princess Sleep-Bringer" by mothy. More specifically, the character who sings it, Margarita Branchenheim (played by Vocaloid Hatsune Miku).
Emilie Autumn: Compared to her other, much deeper songs about sadness/depression, "Willow" can come off as this.
Mr. Smiley from the Mustard Plug song of the same name is a variation of the classic smiley-face badge thing. A Type C - he goes nuts and kills his entire family.
Nick Cave's "Good Son".
The subject of "Everybody's Fool" by Evanescence is somewhere between Type A and Type B. In the video, the dissonance between the facade and the emptiness inside results in some Rage Against the Reflection.
Insane Clown Posse's "Mr. Happy" details the day-to-day life of a friendly serial killer who is all smiles unless deprived of victims to strangle.
David Bowie's "D.J." is sung from the perspective of a Type B radio deejay who's "got believers" but is losing his mind and approaching Type C status; the Concept Video contrasts his happy public facade with his increasingly violent, despairing nature in-studio. "I am a D.J., I am what I play/Can't turn around, no, can't turn around..."
Although I laugh and I act like a clown Beneath this mask I am wearing a frown My tears are falling like rain from the sky Is it for her or myself that I cry?
Queen's "The Show Must Go On" describes a Type B (it could also fit a Type A, but Type B fits better)
Inside my heart is breaking
My make-up may be flaking
But my smile still stays on.
For what it's worth, the Reality Subtext (the song was written and recorded as Freddy Mercury as entering the final stages of dying of an AIDS-related illness) heavily supports a Type A interpretation of someone desperately trying to put a brave face on tremendous pain and unhappiness.
The Simon and Garfunkel song "Richard Cory," based on the Edward Arlington Robinson poem. The song's chorus, an Everyman wishing he could be Richard Cory, becomes ironic when repeated one final time after we learn about Cory's suicidal depression.
The protagonist in Jonathan Coulton's song "Good Morning Tucson", a morning news anchor who keeps his trademark smile going even as he's trying to get through his day's work, interviewing guests he doesn't particularly care about, and literally setting the studio on fire, watching it burn down around him.
Siouxsie and the Banshees' "Happy House".
The song "The Great Pretender" describes this kind of person, who puts on a happy facade to hide their sadness about losing a lover.
The Rise Against song "The Approaching Curve" is about a relationship built around this trope by both sides; the relationship is falling apart, but according to the lyrics "They'll remember, only our smiles 'cause that's all they've seen. Long since dried, when we are found, are the tears in which we had drowned..." Overall, it makes the song about a tough breakup even sadder than it was before.
"Go Away" by Delain is a "The Reason You Suck" Speech to a Type A, a person who puts all their effort into putting on an act instead of solving their problems.