I've also got a 2001 Wrangler sport (60th anniv) and I have similar issues. I know it's not an incorrect amplifier installation or hookup, as I've done several and rewired mine at least twice. I'm not too sure about the alternator of the wrangler, but I'm betting that it would be pretty stout as aftermarket add-ons are pretty common (winches, fog lights, etc.)

(edit:the stock stats are a 117 amp alternator and a 500 amp battery)

How would the capacitor be installed? Just a decent sized cap just before the 12v+ terminal and gnd? Wired in parallel, like a sound reinforcing cap for sub amps?