This is how I remember the song as my father sang it to me in the early 50s. I never heard any verses, just the chorus. As a preschooler, I probably misunderstood some of the words, but here's the pseudo-phonetic best I can do:

Karo, kiro, me dairy-o
Me-ha-me-ho
Rum-a-stick-a-bum-a-diddle
Soot-a-pack-a-penny-whittle
Nipkin, catnip, sing a song
Kitchie, kitchie ki-me-oh