"The Eddystone Light", Heine's "Die Lorelai" and Stephen Foster's "Beautiful Dreamer" are the songs involving mermaids that spring to my mind, whereby only the first is a comic song. "Die Lorelai" is witty and ironic, which doesn't quite come across in the melody. I don't think I've ever heard it in English. I suppose a Lorelai isn't really a mermaid, but she's fairly close.