I don't know of too many songs that were banned from radio airplay in Australia. I certainly remember Snoopy vs the Red Baron being played with a beep censoring out the word bloody. I doubt the beep version is online but it is not a bad tune. I can't listen to it without mentally adding in the beep.
Skyhooks walked a fine line at times and I believe Smut was banned.
One eighties song I liked very much was Frankie Goes to Hollywood's Relax. It was banned by the BBC. Not sure about here, but I can't remember hearing it on air.
What about Lou Reed's Take a Walk on the Wild Side? Was that banned?
All pretty mild stuff compared to what now passes as music known as rap.
I can't think of any more. There was probably a good bit of self censorship by radio stations, especially those with conservative owners. Do you know of any other banned songs?