The word "coon" can be used in a derogatory way, yes, no one is disagreeing with that. But when the song was made, it was just some random word or phrase the guy said to be funny, like Yakety Yak or Do-Wacka-Do.

"'coon' was originally a short form for raccoon in 1741... then by 1832 meant a frontier rustic (a white person from the country), and by 1840 a Whig. The 1834 song 'Zip Coon' (better known today as 'Turkey in the Straw') didn't refer specifically to either a White or a Black and the 'coon songs' of the 1840s and 50s were Whig political songs. By 1862, however, coon had come to mean a Black and this use was made very common by the popular 1896 song 'All Coons Look Alike to Me,' written by Ernest Hogan, a Black who didn't consider the word derogatory at the time."
Extract from 'I Hear America Talking' by Stuart Berg Flexner: