To venture a guess, I am thinking the song you are looking for is a derivative of "Frog Went A-courting" with a form of the "kimo" version of the refrain. Randolph in "Ozark Folksongs" has a text called "Uncle Rat's Courtship" in which it is Uncle Rat who is doing the courting but the rest of the song is a selection of the innumerable verses from the frog version. The frog song itself comes in two distinct forms. One has the hum refrain, while the other has a nonsense lyric refrain that often includes the word "kimo" or a sound-alike such as "Kaimbo" in the one you encountered.

Some examples of the nonsense refrain include:

Ki-mo, kemo, ki-mo, kee Way down yonder in a holler tree An owl and a bat and a bumblebee King kong kitchie kitchie ki-me-o