Because songs are part of the core information of a Radio Airplay artist account, individual songs can't actually be fully deleted from Radio Airplay account pages - this can only happen when an entire account is being closed down, and all its information removed.
On your account ARTIST CONTENT > SONGS page, each song has an "Edit Song" option. Place your mouse/pointer over "Edit Song", and you'll see the "HIDE" and "RENAME" options. Click on "HIDE".
You will see a Pop Up where you will need to click OK to proceed:
Once you HIDE a song, this is what removes the song from view and play on Jango Radio. Hidden songs only exist within your private Radio Airplay account page, at the bottom of your Songs list, in the "Hidden" status, not affecting your plays or stats. Only the "LIVE" songs in your account will be playable and exist on Jango Radio.
It's also recommended to RENAME a song before Hiding it, adding something like "(Hidden)" or "(Old Version)" to its title - just as a reminder for yourself, so you can better differentiate your LIVE and HIDDEN songs within your Radio Airplay account page.
To Rename an already-Hidden song, first "Show" the hidden song. You'll then be able to "RENAME" it, and then "HIDE" it again. Hidden songs can always be restored to your Jango Radio page, by using that “Show” option.