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"Coat of Many Colors" from Joseph and the Amazing Technicolor Dreamcoat desribes the many colors of Joseph's coat note Red, yellow, green, brown, scarlet, black, ochre, peach, ruby, olive, violet, fawn, lilac, gold, chocolate, mauve, cream, crimson, silver, rose, azure, lemon, russet, grey, purple, white, pink, orange, and blue. Listen to Ned Flanders of The Simpsons sing part of it here.
"The Colors of My Life" from The MusicalBarnum - sung by the titular character and then as a Dark Reprise by his wife, who prefers more mundane colors.
While the songs themselves don't mention colors in any extreme way ("Nothing Like a Dame" does have the line "We feel restless, we feel blue", but that's about it), the film of South Pacific made the rather odd decision to gel the camera during the musical numbers. When the sky suddenly turns pink, you know there's a song coming up.
"The Green with Envy Blues" and "The Spectrum Song" from Disney's The Wonderful World of Color.
The version of the Spectrum Song featured on Walt Disney's Wonderful World of Color features an additional bit:
Ludwig Von Drake: Now, alright, we know that everybody don't have television sets with color, so... we're gonna do a version for them, we don't want you to feel left out of it. Here's for you... Black black gray white gray gray gray white white white gray gray white, black. Black black gray white gray gray gray white white gray gray gray black, black. Alright, now you're happy? You don't feel left out? Now I wanna get back to my song.
In the pilot of Darkwing Duck, Gozalen sings a lullabye her grandfather taught her to Darkwing since he doesn't know any, which is mostly singing random colors that exist in the rainbow in a seemingly random and redundant order. That is until Darkwing notices that her grandfather's Zero Point interface cannon has a color coded keyboard.
In Class of 3000, we have "A Richer Shade of Blue" and "The Crayon Song".
"Color My World" by Petula Clark
"(I Like) Traffic Lights" from Monty Python's Contractual Obligation Album.
"Grace Kelly" by Mika, at least in its chorus.
"Bold as Love" by Jimi Hendrix
"I'm Tickled Pink" by Jack Shaindlin, mostly notable for appearing in Fallout 3.