I understand your stituation. In our family room, I have a single 10" sub (a 15+ year old NHT SubOne) in there as part of a 3.1 system. The room is open to pretty much the whole house, so to give it what it really needs would exceed the WAF really quickly, but it's mostly TV watching and casual viewing in there anyways. If SubOne died today, I would probably replace it with a RSL Speedwoofer 10s due to it's small dimensions and good reviews. It's a small sub, and not going to be enough for a huge room, but it's generally considered the best $400 sub on the market. The best $300 sub is often considered to be the BIC Acoustech PL200 II and it's on sale for $250 right now, so if you can get approved by the wife it's your best bet. If the BIC is just too large, the Klipsch mentioned above would be better than nothing, just so long as you have the right expectations for a single inexpensive 10" sub trying to fill a large space.
There is a sticky thread on the Sub-woofer subforum about budget (<$300) subs, that might be worth scrolling through.
7.1.4 Theater Room (In Progress): JVC-RS46U, Silver Ticket AT 2.35:1 142”, Onkyo RZ830, Anthem PVA-7, Panasonic DBT-110, JBL Studio 270’s, 4 - 15" DIY Sealed Subs
3.1 Living Room: Samsung 64” F8500 Plasma, Anthem MRX 300, Dynaudio Audience 52’s, Dynaudio Audience 122C, NHT SubOne