perhaps the dayton sub-800 subwoofer for $79 http
/www.cnet.com/news/dayton-audios-almost-too-good-to-be-true-sub-800-subwoofer/ or
http/www.parts-express.com/dayton-audio-sub-800-8-80-watt-powered-subwoofer--300-627 which would be good if you have decently powered speakers.
generally, any $50 and under subwoofer is going to be rather hit or miss and you're more bound to get hurt than helped. however, if those edifier speakers are rather small and with weak output perhaps staying small and cheap wouldnt be a bad idea.
what you are looking for is a powered subwoofer. all of those have integrated amps. the unpowered subwoofers (passive subs) are ones needing external amplification.