Here is a list that has been put up on a couple different websites, allegedly from a lifeguard at the park. Most of them sound right. There are separate loops for Typhoon Tillies and leaning palms. I'm sure one of them is the Rio Grande shanty heard here:
http://www.youtube.com/watch?v=b0p0IEHb9is
Jamaica Ska- Annette Funicello
Gypsy Surfer- The Avantis
Don't Worry Baby -The Beach Boys
Sloop John B -The Beach Boys
Surfin' USA -The Beach Boys
Surfin' Safari -The Beach Boys
Hawaii -The Beach Boys
Bullwinkle Part II -The Centurions
Pipeline -Chantays
Shake 'n' Stomp -Dick Dale and His Del Tones
Surf Beat -Dick Dale and His Del Tones
Riders In the Sky -Dick Dale and His Del Tones
Hava Nagila - Dick Dale and His Del Tones
Under the Boardwalk -The Drifters
Mr Rebel -Eddie & The Showmen
Underwater -The Frogmen
The Lonely Surfer -Jack Nitzsche
Little Old Lady From Pasadena- Jan & Dean
Ride the Wild Surf- Jan & Dean
Surf City - Jan and Dean
When Salome Plays the Drums- Jimmy Buffett
He Went To Paris -Jimmy Buffett
Fins -Jimmy Buffett
Middle Of The Night -Jimmy Buffett
Margaritaville -Jimmy Buffett
Volcano -Jimmy Buffett
Surf Rider -The Lively Ones
Surfer's Stomp - The Mar-kets
Out of Limits - The Marketts (Ed.-Not the same band... I checked)
In the Summertime- Mungo Jerry
Bread and Butter - Newbeats
(Sittin' On) The Dock Of The Bay -Otis Redding
Penetration -Pyramids
Boss -The Rumblers
New York's A Lonely Town - The Trade Winds
Surfin' Bird -The Trashmen
Walk Don't Run -The Ventures
Wipeout -The Ventures