You will generally need a licence from APRA, covering the public performance of the music on the tapes, and a licence from PPCA, for the public performance of the sound recording. For more information about the APRA and PPCA licences (including the circumstances in which you will only need an APRA licence), see the section above on playing recorded music.
Note also that you will generally need permission from relevant music publishers and record companies to copy a commercially produced recording to use as a backing tape, although AMCOS may be able to provide a licence on behalf of its member publishers.
If you record your own backing tape of copyright music, you will only need licences from APRA and AMCOS.