Others have asked for portable versions of music players (i.e., foobar, winamp, QMP) and some of these have been misquoted as "open source" rather than closed source freeware.
I would like to suggest musikCube (http://musikcube.com/) as an open source, media library based, music player worthy and available for changes to the source code to make it portable. It uses BASS libraries and SQL Lite database and is very lightweight and fast. Currently it takes a multi-user approach, saving settings in a users "My Documents" folder. It also currently does not allow for relative path specification to synchronize its media library with. Many at the musikCube forums have requested such a feature.
I am sure Casey, the project developer (avatar3d screename) would be more than willing to see musikCube modified for such usage.