Adding a cap (capaciter) should solve the problem¿
The cap charges up in between large beats and the sub uses that power when it comes to a hard point in the song instead of drawing that power from the lights or other electrical sources.
An alternator upgrade would have some pro's and con's
Pro: More amperage for your stereo system. You don't run the risk of draining your battery during heavy stereo usage and short trips.
Cons: Extra weight, cost of buying a new alternator.
I think the cap would be cheaper than buying a new althernator, but I could be wrong.
EDIT: rooz beat me to the punch line