Jayne left a comment on the original chords for Sesame Street suggesting an easy version of the chords. And, since it’s a song the kiddies might be interested in playing, I thought I’d go for it.
For the first part you can use:
d – d u d – d u
For each chord until you get to G7. Then do just down strums for that. Back to the pattern for F7. Then just one down strum for the G7, Bb and F. After that you’re back to the pattern.