I found a Singable Picture Book TREASURE and it’s Sesame Street to boot!

The Songs of Sesame Street in Poems and Pictures
Words (and Music) by Various Artists
Illustrated by Normand Chartier

Soooooo many wonderful songs came out of Sesame Street and this book is chock full of them and they are all singable.

The icing on the cake for me is that someone in the WIKI world (though, one must be a bit leery of and check the facts of WIKI articles) has done most of the research work on this book already!

Check out: http://muppet.wikia.com/wiki/The_Songs_of_Sesame_Street_in_Poems_and_Pictures

This link lists all the song with additional links to pages about the history of each song, who sang it, when, and in what context.  WOW!!

The song list (in the order the poem appears in the book):
“Sesame Street Theme” (printed on both end papers)
“The People in Your Neighborhood”
“Rubber Duckie”
“Lullaby But Not Goodnight”
“I Love Trash”
“Still We Like Each Other”
“Wonderful Me” (first two verses only)
“Counting Is Wonderful”
“Ten Cookies”
“Goin’ for a Ride”
“Imagination and You”
“In My Coloring Book”
“What Do I Do When I’m Alone?”
“The Grouch Song”
“Special”
“Up and Down”
“Fur”
“My Street”
“You Are My Neighbor”
“When I Was Little”
“When Will My Birthday Come?”
“Member of the Library”
“Proud to Be a Cow”
“Everyone Makes Mistakes”
“Questions, Questions”
“I Still Love Him”
“That Furry Blue Mommy of Mine” 

Each poem gets its own page and its own illustration.  Soooooo MUCH FUN!!

The printed sheet music for many of these poems/songs can be found in,

The Sesame Street Songbook –
64 Favorite Songs
Featuring Songs and Arrangements by Various Artists
Illustrated by David Prebenna