From the bottom, you need to unscrew and remove both the cover and battery before the aperture for connecting the serial port becomes visible. The battery is a very snug fit in the compartment and appears to virtually block off the hole to this socket.
If I was going to do this mod, and I may well do, then I'd be thinking of trying to mount a mini socket of some sort alongside the 9v power connector on the rear edge. Then I'd make a small adaptor to plug into the mini socket with 9-pin serial connector (including RS232) on the other end.
If, however, you don't want to drill holes or make this a permanent feature, there may be just enough space to curl the four wires around the underside of the battery but you'd need to leave the cover off for the cable to exit...
Good luck!
RDP