I managed to compile the TinySID library for the CUI32. This library can play music from the Commodore 64 by emulating its 6502 CPU and 6581 SID (Sound Interface Device). Everything is done in software -- no additional hardware is needed.
Usage: Connect a headphone or line-in to the RD0 pin. Different tunes can be selected by pressing the PROG button on the CUI32.