How can I add a "C" common wire to this system?
In the wiring diagram in the PDF you linked, the BR (brown) wire connected to the secondary side of the transformer would be your "C" wire.   It connects inside the cabinet to the pump and fan relays, and comes out of the cabinet to the A/C condensor control (along with the "Y" wire from the thermostat).

This post on RadioThermostat's forum discusses a similar issues (no affiliation, except I have one of their thermostats).