Is there any way to acquire -12 V from +12 V?
Label the wire which is currently ground "-12V".
Label the wire which was previously 12V "GND".
(There is no step 3)


To test: Connect a DMM's ground lead to the wire you've labeled "GND".  Connect the positive lead to the wire you've labeled "-12V".  The display will read -12 volts.


Of course, this won't work if you've got any other signals referenced to the original ground, so it's rather tongue-in-cheek.  Just wanted to point it out in case it wasn't obvious.

More seriously, my solution would be a charge pump driven by an RC oscillator.  Without transistors, this will limit you to the output current of your opamps.  On further consideration, it might not be possible due to the problem of bootstrapping your opamp power supplies.