Knocking On Heaven's Door
2 verse, 2 chorus, 3 chords.
Yep, there's a good one.... except there are really four chords - I, ii, IV, and V.
In the key of G, it goes
G D Am Am
Knock knock knockin on heavens door
G D C C
Knock knock knockin on heavens door
The chord progression is repeated throughout the song (I-V-ii ; I-V-IV).
G = I
D = V
Am = ii
C = IV
However, since Am is the relative minor of C, they sound alike and you could probably play the song with 3 chords using just one of them (C or Am) if they're strict with the rules.
Try something in the key of A or G, I find that i do ok in those keys, other than that just find a song that fits your range. I can't sing worth a #@!&%$ but i find i can sing some songs better than others--try little red rooster or something like that or make up your own song ( good idea Rollinrock) -good luck-the dog
House of the Rising Sun?
There are several different versions so maybe there is one that matches your criteria, although I am not sure. Finger picking is always fun and might get you some extra points. :D
Sam Hall by Johnny Cash....it's an easy 3 (C,F,G...in the key of C) chord song. I like the little walk up he does on his way to the G.