I love songs about mermaids! I mean obviously! But honestly there aren't too many just about mermaids, but there are some that mention mermaids at least.
Here's some of my favorites:
Regina Spektor - Mermaid (it's perfect! She even talks about how her feet bleed a la Hans Christian Anderson's Little Mermaid)
Joni Mitchell - Carey
Sedna - Heather Dale
Donovan - Atlantis and Celia of the Seals (about a selkie?)
Shel Silverstein - Mermaid (more of a poem, but it's about the mermaid problem)
Sinead Lohan - I am no Mermaid
Clancy Brothers - The Mermaid
Tori Amos - Silent All These Years
The Lonely Island - I'm on a Boat (T-Pain apparently had relations with a mermaid)
Flight of the Conchords - Mermaid
Did you notice the Monty Python coconuts (horses)?
And of course there are songs from Disney's Little Mermaid movies and broadway show, and old folk songs/sea shanty's that I have no real way of obtaining.
Besides mermaid songs, I also enjoy other sea-themed songs.
Into The Ocean- Blue October
Somewhere Beyond the Sea - Bobby Darin
Undersea Community - The Avalanches
La Mer - Nine Inch Nails
Rock Lobster - The B52's
Sea of Love - The Platters
Octopus' Garden and Yellow Submarine - The Beatles
Ocean Size - Jane’s Addiction
The Beautiful Briny Sea - from Bedknobs and Broomsticks
Island in the Sun - Weezer
Double-O Seafoam - the Neptunas
City by the Sea - Terminal
Santa Monica - Everclear
Gay Fish - Trey Parker
There are of course way more sea themed/beachy songs than mermaid ones, but there you go.