Many of the 2 chord songs can be learned with the easy versions of the chords and therefore can be learned in 1 class. What a way to hook your learners on guitar!
For example, here is the regular way to play Em, and C respectively.
Here are the same two chords, the easy way! They sound the same because they have all the pitches they need to be that chord just without the deeper timbre of the regular ones.
D doesn’t have an easy version and it is for this reason that I sometimes start with a song that has D in it and use the easy versions for the rest of the chords in the song. It might take them another class to be able to do it but hey, then they know D!
Eleanor Rigby by The Beatles (C, Em)
Songbird by Oasis (G, Em)
Best Day of My Life by The American Authors (D, G)
Lean on Me by Bill Withers (C, F, G7)
Sweet Home Alabama by Lynyrd Skynyrd (D, C, G)
Down on the Corner by CCR (C, F, G)
Free Falling by Tom Petty (Capo on 3, D, Dsus4, Dsus2)
Bo Diddley by Bo Diddley (E, A)
A quick google search will yield you hundreds more 2 and 3 chord songs but these are just ones that I use or have used in the past.