Musical Subwoofer for 2 Channel System BUT....

I have an integrated amplifier (Karan Acoustics i180) with no sub out: only inputs and the speaker posts.

Does anyone have a suggestion for a great musical sub that is both (1) smaller (I used to have a paradigm pw-2200 that was great but huge) and (2) would work with this setup? I am looking to spend under $1000, new or used, and the amp is paired with KEF Reference 1 speakers. Oh, and I listen to a wide range of music, but tend toward Blues, Jazz, and female vocalists (e.g., Nina Simone, Natalie Merchant, Margo Timmons).

Thanks, really, for any help.
Rel Strata Mark 3. Reviewed on Audiogon by Quadophile:
Rel Strata Mark III, review by Quadophile
i used to own a rel strata III and it was a very nice sub for music. it has one of the best (if not the best) crossover networks of any sub.
VBT Magellan
Von Schweikert VR-S/1. Powerful and very quick. Relatively small too.