Rumple up a gump stump
coon in the holler
rake a snake a junebug
stole a half a dollar
Was your dad from Louisiana, Peter? Words like "coon" and "holler" sound right for the SE US. Here is the link for a song by Louisiana Red, called "Cootie in the gump stump".It's an MP3 from Amazon, so it should only cost you a buck:
http://www.amazon.com/Teddy-Bear-Cootie-Gump-Stump/dp/B000QNK1SM
"Gump stump" sometimes has the same meaning as "ying Yang" and I assume that both are euphemisms for "anus": "He had money coming out the gump stump" If you simply Google that phrase, you'll see a number of references to it with this interpretation.
I think that that is not the meaning here, though. Did you ever hear the song, "Racoon's got a bushy tail"? Me neither, but apparently it contains this verse:
Rabbit up in the gum stump,
'Coon in the holler,
Possum in the 'tater patch,
Fat as he can waller.
Here's the link for that one:
http://www.timpoe.com/songs/raccoon2.html
I would guess that your dad only vaguely remembered the original song and made up nonsense phrases like "rake a snake a junebug" (nice assonance!) to fill the gaps.
Thank you. I really enjoyed researching this. There was nothing remarkable involved in the research. Since you had struck out with the compete verse, I simply chose phrases that seemed as though they might belong to a song. And Google is my
special friend.