First, how many watts are going to be running to those two twelves? It would also be helpful to know what amp fuse the manufacturer of the amp recommends. And second, what is your cars voltage at the battery on idle now? This will depend a lot on what you should do.
In my car the pulleys killed my voltage. On idle it was sitting at 12.2 volts. On a normal car this won't hurt all that much. If your running a stereo, however, this will kill you. It is not good for your stereo. You will lose sound quality and the stereo will probably drain your battery a lot at idle. This is not to mention the extra wear and tear running at a lower voltage puts on your amps.
IMHO a capacitor would only be a bandaid if this is the situation. That is why the voltage your car is at now, is so important. If your voltage is at or above 12.7 or 12.8 on idle, a capacitor would be a good addition. Maybe a extra battery depending on how much power you are pulling. If your voltage is lower than that, I would change the pulley out. The reason for this is that the weakest link in a charging system will bring the other components down to it's voltage (I've experienced this with my alternator and bad batteries). This will lead to pour performance.
Since the voltage on my car was lower, I kept the underdrive pulleys except for the alternator one. I put a smaller pulley on it, and found a belt that fit with the new pulley. This brought the voltage up to 13.3 on idle. On a normal car a lower voltage wouldn't hurt all that much, but if your running subs you have to address the problem.
Once you figure out your voltage now and what your plans are I can tell you whether a capacitor, battery or both is needed. This is what it took to get my stereo running optimally: 200 amp alternator, 1 3/4" alternator pulley, Two Optima red top batteries, lots of 0 gauge wiring, and lots of fuses. As you can see, this was one of those projects that got way out of hand though