Learn to play this song on the ukulele https://youtu.be/TsFGSZ8tsPw
I actually remember reading the Hop on Pop book when I was in elementary school. I find it amazing that I had the opportunity to read this book to my children when they were toddlers.
Updated 2/13/2016, chords as requested by Vansheryline Keo.
All of the "verses" use the following pattern: A C#m7 Bm7 E7
For example the first 2 pages are:
[A]Up [C#m7]pup, [Bm7]pup is [E7]up. [A]Cup [C#m7]pup, [Bm7]pup in [E7]cup. [A]Pup [C#m7]cup, [Bm7]cup on [E7]pup. A C#m7 Bm7 E7
Keep doing that until you get to the "He Me" page. On that page you change to the following:
[Bm7]He [C#m7]me [Bm7]He is after [C#m7]me
[Bm7]Him [C#m7]Jim [D]Jim is after [E]him.
Back to the A C#m7 Bm7 E7 chords until you get to the page that has "Pat Bat." When you get to that to the same chords you played for "He Me." Then after the "Don't sit on that" line go back to the A C#m7 Bm7 E7 chords.
That's about it (I think).