M. Ted, I agree that the name of the dance "coon-jine" and perhaps some of its movements have their source in the Congolese or West African traditional dance, "counjai" {Counjaille}.

However, I believe that the referent "coon" comes from the referent for the animal called "racoon". See this excerpt from an online article among many others:

"Many slang terms use the term "coon" to mean raccoon. Their black eye-mask and nocturnal habits suggest anthropomorphic parallels, so we get the term "coon" meaning to steal or pilfer, for instance. The word also was used in the 1830s to mean a rustic, a country-bumpkin. In 1840, the coon was the figurehead of the Whig Party. (Where are the Whigs now when we need them?)

Unfortunately, many of those negative stereotypes were applied to black people, hence the derogatory term "coon," first used in the 1850s but more commonly heard after 1890. Some etymologists speculate that the term was used because of the raccoon's dark coloring rather than its real or imagined behavior. Whatever the case, the usage is highly offensive today - heck, it was highly offensive back then. For that reason, "in a coon's age" makes many people uncomfortable, notwithstanding its innocent origin"...

http://www.straightdope.com/columns/read/1536/whats-the-origin-of-coons-age

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I believe that it wasn't just the dark coloring of the racoon, but also their white circled eyes that fed into or helped create the caricature of big, wide bulging eyed Black people {for instance Stepin Fetchit}. See this excerpt from the biography of
Lincoln Theodore Monroe Andrew Perry [Stepin Fetchit]:

.."The "Coon" persona mitigated the low status accorded African Americans by whites by feigning near-idiocy in order to frustrate whites by ironically fulfilling their low expectations. (The "Tom," by contrast, is praised by whites for his good work and loyalty. A parallel racial caricaturization of black men by whites, the "buck," is the repository of their racial and sexual fears, and still can be seen in blaxploitation movies of the 1970s and currently, in the gangsta rapper.) Perry used this mitigation stratagem when dealing with whites in real life, allegedly maintaining a coon persona while auditioning for a role in the film "In Old Kentucky," where he stayed in the Stepin Fetchit character before and after the audition. Often, while making movies in which he found the lines offensive, Perry would skip or mumble lines he did not like, pretending to be too stupid to comprehend the script.

The "Coon" stereotype existed long before Perry decided to adopt it (its prevalence as a defiance stratagem intensified after the gains that African Americans had made in the post-Civil War Reconstruction Era were rolled back by segregationist Jim Crow laws, when an "uppity" African American might find himself at the end of a rope). However, he was such a hit with white audiences that his Stepin Fetchit persona popularized the "Coon" image to an unprecedented degree in the medium of film, and many stereotypical black movie characters, including the child Stymie in the "Our Gang" comedy series, were based upon Stepin Fetchit to cash in on his popularity."

http://www.imdb.com/name/nm0275297/bio