I was going to mention The Band Played Waltzing Matilda, but I was beat to it.
Does The Green Fields of France count?
Richard Thompson has a great background in folk music of the British Isles. And he’s used that background to write some memorable stuff. Like The End of The Rainbow:
Check out his Song-O-Matic for lots more stuff with a bit of grimness…
Ironically, many (if not most) of those hillbillies (at least in Appalachia) can thank their Celtic roots for that… 
There’s this line from “The Rebel Sons of Erin”-
Now it’s said in terms of love and war
That the Irish are quite mad
For their songs of war are merry
And their songs of love are sad
Puff the Magic Dragon makes me sad- he’s left all alone in his cave when his boy grows up…
That’s presumably inspired by Chesterton’s The Ballad Of The White Horse.
“For the great Gaels of Ireland
Are the men that God made mad,
For all their wars are merry,
And all their songs are sad.”
I’ll put a nod in for Peter Jones’ ‘Kilkelly, Ireland’. My mother banned me from playing that song at her house because it makes her weep every time she hears it.
Is there even a possibility that the Irish (or Irish descendents) won’t win this one? They may not have invented misery, but they sure perfected it.
You can be a gambler
Who never drew a hand
You can be a sailor
Who never left dry land
You can be Lord Jesus
All the world will understand
Down where the drunkards roll
Down where the drunkards roll
My favourite version of this song is the cover by an Irish lass, Maura O’Connell.