Are there any software have function "stereo swap + background playing"
I have tried aeroplayer and pockettunes,
but both of them do not have stereo swap function.
and tcpmp can not set to background playing mode.

Any recommendtion?

At the moment, none of the most common audio apps for Palm have what you're looking for. PocketTunes and AeroPlayer are supposedly the most feature-rich players around but they don't have the stereo swap feature that you're looking for. A newer player that a lot of people are appreciating is Busker[url=www.electricpocket.com/products/busker.html] or as it was called earlier GoMP3. Even this one though doesn't have the stereo swap feature.

So. I', afraid you're currently out of luck. If you do run into a solution, short of re-encoding your music files and swapping the channels, do let us know by posting here.