Irony

Please Don't Leave Me ~ P!nk
This song uses situational irony because the narrator starts off by saying how she hates this guy: "I don't know if I can yell any louder/How many times have I kicked you out of here?/Or said something insulting?" So the expected result is that this is going to be a break-up song, because that is what the lyrics imply. Contrary to the expected result, the chorus goes on to say "please don't leave me," because she loves him and cannot live without him. Because this is not expected, this song is situationally ironic.
Lyrics

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Smile ~ Lily Allen
This song has situational irony because the singer starts singing about her cheating boyfriend and how she was devastated at first ("I just sat by myself all day"). But then the tables are turned: he wants her back and she just smiles at his pain ("When I see you cry/It makes me smile"). This is kind of an unexpected twist. Another way that this song is ironic is that the lyrics are kind of depressing/disturbing: they're about cheating and laughing at people's tears, etc. But the music is all upbeat and happy-sounding, so there is a definite contrast there.
Lyrics