Awesome! I love Kermit the Frog! And I love his songs. There's definitely a number of great ones you could include both from The Muppet Show and Sesame Street and a lot of the others shows and movies and specials he's been in.
I like the list so far. I might could do Youtube links later, but here's a few other favorite Kermit songs for me.
And of course, "Being Green" and "The Rainbow Connection" are absolute musts!
"Sweet Vacation" from The Jim Henson Hour
Pig Calypso (Pigs Having Fun) from The Muppet Show
Lime in De Coconut from The Muppet Show
Disco Frog from both Sesame Street and The Muppet Show
Everyone Matters from It's A Very Merry Muppet Christmas Movie
(I love Christmas! And "The Christmas Wish" is such a great song, so I'm glad you got that one on there, along with "I Believe in Santa Claus" I think this is another great one to include too.)
I Love My Elbows from Sesame Street
The Frogs in the Glen from Sesame Street
Do Op Hop from Sesame Street
African Alphabet from Sesame Street
Alphabet in the Swamp from Sesame Street
Get Along from Sesame Street
You're Alive from Sesame Street
Tadpoles from Sesame Street
This Frog from Sesame Street
My Pollywog Ways from Sesame Street
Do De Rubber Duck from Sesame Street (okay, so this is a menagerie of Muppets, but Kermit is in the mix)
When You Were a Tadpole and I was a Fish from The Muppet Show
Just One Person from The Muppet Show (okay, so this was a number of the Muppets, but Kermit was in there for it)
Kokomo- as covered by The Muppets (from "Muppet Beach Party" album) (Kermit & Piggy song)
She Drives Me Crazy- as covered by The Muppets (from "Kermit Unpigged" album) (Kermit & Piggy song)
Jingle Bells/Jingle Bell Rock from Muppet Family Christmas
Carol Sing from Muppet Family Christmas (this is a whole ton of Muppets, but of course Kermit's in there- and it certainly would be a nice addition for a CD as a Christmas gift. And if you can get the original uncut version that would be really cool as it includes Statler and Waldorf singing one of my all time favorite Christmas carols- "I Heard the Bells on Christmas Day". Awesome!)
For that matter, "We Wish You A Merry Christmas", "Deck The Halls", "Have Yourself a Merry Little Christmas", "The Twelve Days of Christmas" and definitely "Silent Night, Holy Night" would all be ones I'd want to include even though Kermit doesn't sing on all of them. And "The Peace Carol" and "A Baby Just Like You", all from the "John Denver and the Muppets: A Christmas Together" soundtrack. (I really LOVE that special!)
Of course, I love Christmas and Kermit so much, I would probably just wind up including the whole of the "John Denver and the Muppets: A Christmas Together", "Muppet Family Christmas" and "The Muppets' Christmas Carol" soundtracks.