Since you already have +12V, you really just need to get -12V. A smps chip, along with a bit of supporting circuitry, can do that rather easily; the idea is to, first allow, and then to stop current through an inductor. When you suddenly stop the current feeding the inductor, the magnetic field created by the current induces current to continue to flow. This generates a big negative voltage spike, which, if captured using a diode, can be used to create a -12V supply rail. Feedback controls the oscillator which is alternatly starting and stopping the current, and thus the output is regulated.
However, rather than have me describe it to you, look at the linear site for inverting regulators here: