I don't think I would go any smaller than 12" drivers for subs, but I have heard REL and KEF subs with smaller drivers that were surprisingly good for their size, but expensive.
I would look at the SVS SB-1000 or get a pair of Rythmik sealed subs for the best sound. The Rythmiks would be a little over budget, but a worthwhile investment. If you can find a different place to hide a small sub and get it somewhere else in the room, the SVS subs might be better. There are wireless options and they come with an app that lets you adjust the sound remotely.