In all fairness it mostly just depends on your expectations. You could build a sub for around 200 dollars and it will be better than anything you could buy for that price. That doesnt necessarily mean it will be a fantastic sub, but it really could be done. The biggest variable will be obtaining the enclosure. If you can build one yourself, or if you'll have to purchase in some way.
PE has the dayton 240 watt plate amp for 110 bucks right now.
You could get the 10" DVC dayton subwoofer for 40 bucks
Go to lowes and get the concrete forming tube for around 10 bucks
You'll need a vent tube and a couple other various parts but you're in under the budget and the sub will perform well. Much much better than anything you could buy at the price. That particular driver has gotten some nice reviews.
Keep in mind, this is no audiophile sub, but represents excellent bang for buck. You'll know its there....