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I put a Kicker self-powered sub in my 89 roadster. It's a tube, 10" speaker, has it's own power feed triggered by the antennae mast power so it's only on when the head end is on. Pickups are from the speaker inputs to the rear speakers, they don't actually take power from the Bose speakers but just copy the signal. It has it's own relative gain control to be adjusted once, and it's own hi/low crossover.
It's a blast and made the Weak-bass Bose sound great for Rock music.
Fits snugly behind the top when it's down, and the sound also comes from the reflex port as well as the main 10" opening. 150 watts.
Here's a little writeup I did while replacing the entire stereo in my '96. Since everything is replaced, the only thing different, really, about your '84 is you should use a single-DIN head unit (or is it 1.5-DIN? I forget).
As for the subwoofer, screw a sub box down to the rear cargo floor, hook the amp up to the head unit's Subwoofer-out jack, and you're golden.
Designer Imagines A Corvette That Looks More Like a Corvette Than the Corvette
Slideshow: A Jaguar designer's personal project imagines what a modern front-engined Corvette might look like if Chevrolet revisited the golden age of the Stingray.