J-boy, I have to disagree a bit about "My Grandfather's Clock." The song is really about a full life, from birth to death. It's only the last verse and the last line of the chorus that are about death. And even the parts about death aren't really sad, with the 90-year-old man & his clock taking their leave surrounded by loved ones.

But some songs that I do think pair rather morose lyrics with tunes that seem too pleasant or happy for the story are:
Banks Of The Ohio   (even the lyrics to the chorus are at odds with the story)
John Hardy
The Baron O' Brackley (Inverey)
Lily Of The West
Mrs McGrath
various incarnations of "Stagolee," "Pretty Polly," "Matty Groves," Binnorie, O Binnorie, House Carpenter, Frankie & Johnny,
Duncan & Brady