Here is a small selection of tiny drivers that could be used for your purpose. For music listening only really as none of these will really reach down into the tactile range of hearing. And if you're an organ listener I'd think about something else too.
http://www.parts-express.com/wizards/searchResults.cfm?srchExt=CAT&srchCat=838&CFID=15963622&CFTOKEN=58479262
I don't know if after I made one of those into a subwoofer if I would want to carry it around with me. It wouldn't be too heavy, just a bit cumbersome unless you threw it in a backpack. It would be decent for a desktop system but that's about it.

Here is a quick design for the tang band 5 1/4" driver (my favorite of the 3). Using a sealed box, which is the yellow plot, you have a steep roll off from the get go. It's usable bass but not much and really doesn't reach very deep. The only major plus side is size that goes with it. It's about 1/4 cubic foot total volume. Your enclosure would be roughly an 8" cube. Still decent sized for something portable. You could always fudge the dimensions and get something that would be more of a rectangle cube and narrow the dimensions some, but you'd still have to leave about 6.25" on each of the baffle sides just to compensate for the face of the driver.
The ported box, while being nearly twice the internal volume, isn't really that much bigger since we're dealing with smaller boxes in the first place. You'll get a more flat response and it'll get louder and your extension will be greater. Downside is trying to reach that acceptable level of port size vs air velocity that will work. Smaller port will take up less real estate inside the enclosure but you'll get port chuffing worse. It's all a series of trade offs.
Quote:
Originally Posted by
Coop 
I once met a guy who made the craziest subwoofers out of cardboard tubes. One of the things he showed me was a long tube about 6cm in diameter, it had a few bends in it and there was a 2"driver in there somewhere and an amp.This odd looking contraption could stir up bass like I had never heard before. So great bass can come from tiny speakers, unfortunately tiny speakers in tiny boxes probably wont do...
That was either a transmission line or some variant of it. You can coax a lot of sound out of something like that and all it's doing is utilizing a certain wave length to manipulate how the driver/enclosure work together.