There's an anti-racist song from the 1920s (I think) which, by modern standards at any rate has an unintentionally non-pc title. It's called Picaninny Rose.

There's also a song from a somewhat earlier era called Lydia The Tattooed Lady.

Again, there's a song, the title of which I can't bring to mind at the moment, about a bloke who courted a very fat woman. She was so fat in fact that when they had sex he had to take a tape measure and leave chalkmarks so that he could find his way back. It had something along the lines of "one day while I was a-chalking and a-measuring, I met a guy with a piece of chalk coming around the other side".

Those three are non-malicious and to me are still reasonably acceptable, with a pinch of salt. However, the American country music industry had a very distasteful arm which peddled all kinds of racist muck, and which stretched way back to the earliest days of country music recording. For instance, there was a character who called himself Johnny Rebel who had quite a career in the 1960s with songs like "Nigger Hating Me" and "Some Niggers Never Die (They Just Smell That Way)". I am also reliably informed, although I've never come across it, that there was one from a bit further back called "All Coons Look The Same To Me".

Finally, there was an appalling stinker, which originated in 1950s/60s Britain, which parodied Island In The Sun, and which consisted of attacks on black immigrants.

If you're thinking of using anything like those, for God's sake hang a big disclaimer over it.