E, A, C, Em, Am, G, G6+9, E7, Am7. I think that is pretty much it with 3 or fewer fingers and no barring and no use of the thumb.
Therefore, any song utilitizing these should be easy.
Most 4 chord songs utilize a I-IV-V VIm pattern in a variety of combinations; you can't do that with above chords.
D G A Bm does the trick.
Jay