I thought about putting up Put on a happy face. It has some more difficult chords. You would need to use all four fretting fingers. It starts with an [Eb6] AKA [Cm7] (same four notes different order (enharmonic).
[Eb6] Gray skies are gonna [Gm7] clear [C7] up, [Fm7] put on a [Bb9] happy [Fm7] face [Bb9]
[Eb6] Brush off the clouds and [Gm7] cheer up, [Fm7] put on a [Bb9] happy [Bbm7] face [Eb7]
[Eb6] = (3333)
[Gm7] = (0211)
[C7] = (0001)
[Fm7] = (1313)
[Bb9] = (1213)
[Eb7] = (3334)
That's just the first two lines. It's not as hard as it looks but most of the chords aren't common. As with many of my files I don't know where I acquired them.