Most trad mermaid songs are about mermaids rather than as can be sung by said amphibians.
Here's a start on a song with apologies to Rawtenstall Annual fair's author.

Roll up, roll up, come and see the mermaid,
see the lovely lady, half a woman, half a fish,
Last time I came ashore I landed on me tail,
A little lad said, 'Mother, I think it's a beached whale,'
Another said, 'A walrus,' another said, 'A seal,'
Another said, 'An octopus,' and then, 'A conger eel.'
A fisherman came up to me and said, 'Have you got a daughter?'
When I answered no, he threw me back into the water,
                   All on ---------- Beach.