In this article, I analyze the vocal melody for 4 different two chord songs: Fire on the Mountain by the Grateful Dead, Something in the Way by Nirvana, Break on Through by The Doors, and Mannish Boy by Muddy Waters. The two chords used in each song varies so you can see 4 examples of how to write your own two-chord song.
I transcribed the vocal melodies of three classic one chord songs: Get Up Stand Up, Spanish Moon and Papa Was a Rollin' Stone. There are commonalities in all three songs. First, they all use either a minor triad or minor 7th chord. Also, they base the vocal melodies around the tones in the chord. I have the sheet music for the vocals for all 3 songs with some quality notes.