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 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.