A catchy down-country rendition of "It Don't Do Nothing But Rain" by Lew Childre:
http://www.youtube.com/watch?v=laGENW6Vobs
This should help fill some gaps in the lyric transcription above.

For comparison, here's the version by Jones & Hare, singing under the names Billy West and Bob Thomas:
http://www.youtube.com/watch?v=b8ULFQad1t8

I also see on YouTube a version by Harry Hudson's Melody Men.