The way I did it was to run an Icecast server from my home machine, and then have the players load that URL into WinAmp, VLC, whatever. It worked decently well, and the quality is much better than trying to stream over the voice chat, since it just sends the original music file out rather than recompressing with a voice codec. The cost is about a 10-second lag when changing tracks.
Running a server on the user's computer with a web application is probably no-go, but it might be something you could do with centralized hosting.