Steve and I started brainstorming and came up with this list:

Carol of the Bells,
Silver Bells,
Grandma Got Run Over By a Reindeer,
The Chipmunk Song,
The Holly Has a Berry,
The Holly and the Ivy,
A'Soulin,
The Wassail Song,
The Gower Wassail,
Do You Hear What I Hear?,
Box of Candy and A Piece of Fruit (Shel Silverstien and Bob Gibson)
Season of Hope by Sandy Andina
Santa Baby (Eartha Kitt)
'Zat You, Santa Claus? (Louis Armstrong)
Its The Most Wonderful Time Of The Year
Lord of the Dance
The Wren
Mary, Did You Know? (Kathy Mattea)
Here Comes Santa Claus
Joy to the World
O Come, O Come Emanuel
I Saw Mommy Kissing Santa Claus
Linus and Lucy (Vince Guaraldi)
The First Noel
It Came Upon A Midnight Clear