Brilliant! 
I’ve sung Parra Hearn (it means “Curing Pilchards”) with a raucous group of fellow Cornish students on a pub crawl around Penzance, but hadn’t heard The Mermaid of Zennor. Thanks for those.
Now here are a couple of historic ones, including one that’s only recently been rediscovered! First, please all stand for the Cornish national anthem, Bro Goth Agan Tasow (“Land of Our Fathers”)…
Full lyrics and translation here.
(And yes, if you’re Welsh, you already know the tune. We nicked it. 
Respectfully, of course.)
This next one unfortunately I don’t have a video for, as I believe it’s never been recorded — it’s called Can Palores (“Song of the Chough”), apparently written by Cornish bard Dr Ralph Dunstan, probably in the 1920s or early '30s. The manuscript of it was discovered in the Morrab Library in Penzance just a couple of months ago and given its first modern performance earlier this month by Cornish choir Keur Heb Hanow! Here’s the story, with an image of the manuscript along with the words and translation: A musical discovery at the Morrab Library
The background to the song is the legend of King Arthur. According to the Cornish version of the tale, when Arthur was mortally wounded in his last battle, his spirit was transformed into the chough — a black bird with its legs and beak stained red from the blood that Arthur shed on the battlefield. Choughs were in decline at the time this song was written, and they disappeared from Cornwall’s cliffs altogether in the 1970s, but since 2001 they’ve been nesting there again and expanding their range. So when you see a chough in Cornwall, you know that King Arthur is still watching over his kingdom! 
(More information on Cornish choughs from the RSPB and the National Trust.)
EDIT: I’ve just searched further and found a more extensive write-up about Can Palores, which includes the rest of the verses — it turns out it’s Dunstan’s setting of a song by Robert Morton Nance, the second Grand Bard of Cornwall, from the end of his play An Balores (“The Chough”). This website for traditional Cornish songs gives the full lyrics, the background story and a clearer transcription of the music! Can Palores — Song of the Chough