Guest Sally's verse reminds me that in the 1950s a working colleague gave me a single nonsense verse he used to sing as a kid:

Coyney nair-oh/Kilt a care-oh/ Coyne-ee
With a bin strin stranna bonna fiddle or a ring
And a ring ding bully dinny coynee.

The tune wasn't related to any version of Kemo Kimo that I've ever heard, but a performance of that song is described and written out in full in J Ewing Ritchie 'The Night Side of London' 1857, as sung by Mrs Caulfield at the Canterbury Hall in Lambeth, London. He gives three verses starting with 'Down in Skytown...' and with the 'Sing song Polly' chorus.

Canterbury Hall was a pioneer music hall of the 1850s and Mrs Caulfield was one of its early stars. Another Canterbury star was the great Sam Cowell, mentioned twice in this thread as a 'minstrel vocalist'. I have never heard him so described and I don't think he ever appeared blackface - and if he sang this song, it wasn't one he was well known for. He was certainly the best known, if not the first, singer of 'Villikens and his Dinah' and 'The Ratcatcher's Daughter' and he popularised 'Billy Barlow' in England.

Kilgarriff's 'Sing Us One of the Old Songs' gives Mrs Florence as another singer and notes a version of Keemo Kimo published in 1854 attributed to George or Edwin P Christy, with music by Woods.