javax.comm, I think, might be what you're looking for.
The serial port only takes care of the data link layer, you need to write/steal a protocol to put on top of that. Here's a bit of a tutorial that might get you started:
http://www.captain.at/howto-java-serial-port-console.php
http://www.captain.at/howto-java-serial-port-javax-comm-rxtx.php
If the computers are Linux (doubt it but it's an idea) you can assign the com port and IP and treat it like you would ethernet, just slower. Then you just need the FTP server and client. I'm not sure if this can be done in Windows though, I've never tried. I remember doing it, but I don't remember how...so it would probably be quicker to write in Java....