Here are the chords according to a song book I have (not the original song sheet):
[C] Roll along Prairie Moon,
Roll a- [Dm] long while I croon
[Dm7] Shine a-[G7] bove
[Dm7] Lamp of [G7] love
[Dm7] Prairie [C] Moon
Way up [C] there in the blue
Maybe [Dm] you're lonely too
[Dm7] Swinging [G7] by
[Dm7] In the [G7] sky
Prairie [C] Moon
I [G7] need [C7] your [F] tender [Fm] light
To [C] make things [A7] right
You [D7] know I'm so alone to- [G7] night
Far a- [C] way shed your beams
On the [Dm] girl of my dreams
Tell her too [Dm7] I've been [G7] true
Prairie [C] Moon [Cdim] [G7]
I'd play it in F, though, on a tenor:
F - Gm
Gm7 - C7
Gm7 - C7
Gm7 - F
With the chorus:
C7-F7-Bb-Bbmin
F-D7-G7-C7
etc.