I did a search at www.deja.com and found these:

1. There's A Rainbow Round My Shoulder - Frank Sinatra (& also by Bobby Darin)
2. Over The Rainbow - Judy Garland
3. Rainbow -Gene Chandler
4. Roses and Rainbows - Danny Hutton

And then I hit the jackpot!

Afterglow-Chasing Rainbows
Teddy Andreas-Busted Rainbow
Blue Magic-Chasing Rainbows
James Byrd-Bay Of Rainbows
Michael Cates-Apres L'Arc-en-ciel (After The Rainbow)
Coloured Stone-Chasin'rainbows
Cowboy Junkies-At The End Of The Rainbow
R. Crumb & His Cheap Suit Serenaders-Chasin' Rainbows
Bruce Daigrepont-Arc En Ciel (Rainbow)
Michael Franks-Antonio's Song (The Rainbow)
Roy Hamilton- (At) the End (Of a Rainbow)
Hammerfall-At The End Of The Rainbow
Indians-Caught A Rainbow
Alan Jackson-Chasin' That Neon Rainbow
Klaatu-At The End Of The Rainbow
Al Kooper-A Visit to the Rainbow Bar & Grill
Mannheim Steamroller-7 Colours Of The Rainbow, The
Melanie-Babe Rainbow
Buddy Montgomery-1,000 Rainbows
Alex Moore-Chasin' Rainbows
Phil Napoleon-Always Chasing Rainbows
Laura Nyro-Broken Rainbow
Osmonds-At The Rainbow's End
Prince Charming-Black Goat Of The Woods With 1000 Rainbow Eyes
Flora Purim-Above The Rainbow
Blackmore's Rainbow-Catch The Rainbow
Riders In The Sky-At the End of the Rainbow Trail
Rolling Stones-Blinded By Rainbows
Seekers-Chase A Rainbow
Kenny Wayne Shepherd-Chase The Rainbow
Lonnie Liston Smith-Colors Of The Rainbow
Sons Of Champlin-Black And Blue Rainbow
Sons Of The Pioneers-At the Rainbow's End
Sons Of The San Joaquin-Boss Is Hangin' Out A Rainbow, The
Spinners-Can Sing A Rainbow
Stockton's Wing-Chasing down a rainbow
Rhet Stoller-Concerto For A Rainbow
Hank Thompson-At The Rainbow's End
Yeskim-Beyond The Rainbow
Afterglow-Chasing Rainbows
Teddy Andreas-Busted Rainbow
Blue Magic-Chasing Rainbows
James Byrd-Bay Of Rainbows
Michael Cates-Apres L'Arc-en-ciel (After The Rainbow)
Coloured Stone-Chasin'rainbows
Cowboy Junkies-At The End Of The Rainbow
R. Crumb & His Cheap Suit Serenaders-Chasin' Rainbows
Bruce Daigrepont-Arc En Ciel (Rainbow)
Michael Franks-Antonio's Song (The Rainbow)
Roy Hamilton- (At) the End (Of a Rainbow)
Hammerfall-At The End Of The Rainbow
Indians-Caught A Rainbow
Alan Jackson-Chasin' That Neon Rainbow
Klaatu-At The End Of The Rainbow
Al Kooper-A Visit to the Rainbow Bar & Grill
Mannheim Steamroller-7 Colours Of The Rainbow, The
Melanie-Babe Rainbow
Buddy Montgomery-1,000 Rainbows
Alex Moore-Chasin' Rainbows
Phil Napoleon-Always Chasing Rainbows
Laura Nyro-Broken Rainbow
Osmonds-At The Rainbow's End
Prince Charming-Black Goat Of The Woods With 1000 Rainbow Eyes
Flora Purim-Above The Rainbow
Blackmore's Rainbow-Catch The Rainbow
Riders In The Sky-At the End of the Rainbow Trail
Rolling Stones-Blinded By Rainbows
Seekers-Chase A Rainbow
Kenny Wayne Shepherd-Chase The Rainbow
Lonnie Liston Smith-Colors Of The Rainbow
Sons Of Champlin-Black And Blue Rainbow
Sons Of The Pioneers-At the Rainbow's End
Sons Of The San Joaquin-Boss Is Hangin' Out A Rainbow, The
Spinners-Can Sing A Rainbow
Stockton's Wing-Chasing down a rainbow
Rhet Stoller-Concerto For A Rainbow
Hank Thompson-At The Rainbow's End
Yeskim-Beyond The Rainbow

Hope those help!