I can think of two right off hand:
“King Kong Song” - ABBA
“Rip Her to Shreds” - Blondie ("…she’s makin’ out with King Kong…")
The Kinks: King Kong; they also mention the big guy in Apeman
Frank Zappa: King Kong (instrumental)
Honorable mention: Jefferson Airplane’s live album Bless Its Pointed Little Head begins with the closing minute of the original movie.
Not mentioned in the songs, but the album Gorilla by the Bonzo Dog Band was “Dedicated to Kong, who must have been a great bloke.”
“Whatever happened to Faye Wray?”
“She got fucked by a 40-foot ape!”
“Bad, Bad Leroy Brown”, by Jim Croce
“King Kong, Your Song” by Bobby “Boris” Pickett
Nick Cave and the Bad Seeds:
King Kong kitchie-kitchie keemee oh!
King Kong kitchie kitchie kee mee oh!
King Kong kitchie kitchie kee mee oh!
King Kong kitchie kitchie kee mee oh!
King Kong did a song entitled “King Kong” on their ‘Funny Farm’ album. But their out-of-print debut album, ‘Old Man On the Bridge’ was a much better collection.
There are the (in-)famous lyrics to the parody version of “You’re the Top”:
You’re the mound of Venus
You’re King Kong’s penis
You’re self-abuse!
“King Kong” by Bow Wow Wow 
Opening song of Rocky Horror Picture Show
Michael Rennie was ill the day the earth stood still
But he told us where we stand
And Flash Gordon was there in silver underwear
Claude Raines was the invisible man
Then something went wrong for Fay Wray and King Kong
They got caught in a celluloid jam
Then at a deadly pace it came from outer space
And this is how the message ran:
Science Fiction - Double Feature…
Bob Dylan’s Farewell Angelina: King Kong, little elves, on the rooftops they dance."
Ballad of Tom Jones: Space fet. Cerys…
Good King Kong Looked Out, from P.D.Q. Bach’s A Consort of Choral Christmas Carols
That repository of pop culture references, “Absurd” by Fluke:
King Kong, in Cannes, on a date with Spider-man
Oooh! cub’s song “New York City”:
Statue of Liberty, Staten Island Ferry, Co-op City, Breakfast at Tiffany’s
Central Park, Brooklyn Bridge, the Empire State where King Kong lived
Coney Island and Times Square, Rockefeller Center
Wish I was there
(In They Might Be Giants’ cover of the song, they sing “where Dylan lived” instead of “King Kong,” because they misheard the lyrics.)
Da Lench Mob’s Gorillas in the Mist
Magilla gorilla ain’t a killa
White boys like Godzilla
But my super nigga named King Kong
Played his ass like Ping-Pong
Rats, I knew I was forgetting something. I even saw them do it live, once.
Passing mention in John Entwistle’s “I Believe in Everything”:
Do you believe in witchcraft, Heaven and Hell,
King Kong, reincarnation,
Fairies at the bottom of the garden…
How about:
King Kong,
The Witch is dead.
Which old Witch?
The Wicked Witch!
King Kong,
The Wicked Witch is dead!
Or were they singing something else?