Woody Guthrie sang about an old army mule with a refrain of Tee-Roo, Tee-roo, (reprat of last portion of last line). A rewrite of a south-eastern version of Devil and the Farmer's Wife.

sort of like:

Maggie (or some other two-syllable name) she was an old army mule
Tee-roo, tee-roo, an old army mule

If that;s the one, I'll try to dig it out. I think it was in the old People's Songbook, if anyone has a copy.