Down in the Valley: C and G7
The Old Gospel Ship: C and G (or C and G7)
Which Side Are You On?: Am and Em
Shady Grove: Dm and C
The Railroad Boy (or The Buthcher's Boy): Am and C
Pastures of Plenty: Am and C (Woody often used only one chord!)
Little Maggie: G and F
Spike Driver's Blues: G and G7 (but with some fancy fingerpicking)

Yes, I know that you can add a third or even a fourth chord to some of these songs, but it is not necessary to do so. Feel free to transpose these to other keys to fit your voice.