The only simpler way that I have encountered is what James Hill does for his beginning classes. He uses D7 and G6 to start.
strings 4321 from top to bottom (relative to the ceiling)
--D7 = 2020
--G6 = 0202
These are fret positions, not finger locations.
This gives a jazzy version of the I chord (G6) and the V chord (D7) for the key of G with the same shape, just shifted back and forth laterally. That works great too -- easily understood by most players, and not much "target practice" for new unsure fingers. Jambalaya is a great starting song, or "How Much is that Doggie in the Window".
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