I am a white liberal American, getting on 75, and I somehow managed to get well into adulthood before I heard that "coon" was slang for a black person, tho eventually I found out that it was all over the English-speaking world. However, I heard "Old Zip Coon" from my mother when I was little, and it is perhaps worth noting that, at least in that version, there is no reference to race in it at all. It is one of those songs that are nominally about themselves:

Oh, there was a man with a double chin,
Who performed with skill upon a violin,
And he played in time, and he played in tune,
But he never played anything but "Old Zip Coon".
"Old Zip Coon" he played all day,
Till he drove his friends away,
And he played in time, etc.

It was, as others on this thread have noted, TTTO "Turkey in the Straw".

Also, on the face of it, there is no reason to suppose that a person called Zip Coon was black (or named after a raccoon for that matter). "Coon" is a well-established surname in English, and a glance at Google reveals that it has various origins -- one of them being as a form of "Cohen"!