Yummy Yummy Yummy by Ohio Express
Who Put the Bomp? Barry Mann
Tie Me Kangaroo Down, Sport by Rolf Harris
They're Coming To Take Me Away Ha Ha by Napoleon XIV
Splish Splash by Bobby Darrin
Shimmy Shimmy Ko Ko Bop by Little Anthony and the Imperials
Rockin' Robin by Bobby Day
Rappin' Rodney by Roger Dangerfield
Pac-Man Fever (Eat 'Em Up) by Buckner & Garcia featuring Jace Hall
King Tut by Steve Martin and the Toot Uncommons
I'm Henry the VIII I Am by Herman's Hermits
Charlie Brown by The Coasters
Bread and Butter by Newbeats
Editing to add that anything by Weird Al Yankovic would fit within the "silly" theme. Also...
Yellow Submarine by The Beatles
Y.M.C.A. by The Village People
Who Woke Snow White Up by The Baha Men
Walk the Dinosaur by Was (not Was)
Walk Like An Egyptian by The Bangles
The Unicorn Song by The Irish Rovers
The Hampster Dance Song
The Fox (What Does the Fox Say) by Ylvis
Supercalifragilisticexpialidocious by Julie Andrews
Sugar Sugar by The Archies
Star Wars Theme/Cantina Band by Meco
Put the Lime in the Coconut by Harry Nillson
Pop Goes the World by Men Without Hats
Octopus's Garden by The Beatles
Mahna Mahna by The Fray
Lollipop by The Chordettes
Kung Fu Fighting by Carl Douglas
Jump In the Line (Shake, Senora) by Harry Belafonte
If I Had a $1,000,000 by The Barenaked Ladies
I Am the Very Model of a Modern Major General by John Reed
Disney Mambo #5 by Lou Bega
Blue (Da Ba Dee) by Eiffel 65
I've Got a Lovely Bunch of Coconuts