I see you quote dollar prices, so I guess you are in the US.
http://www.commonsenseaudio.com/ have a driver 'Audio Nirvana Super 3 Cast Frame' that just sneaks in under your budget @ U$88 / pair. If you buy these they'll give you a box design sheet with them.
Audio Nirvana are about as good value as you'll get anywhere. I haven't heard the 'Super 3s', but I have heard more than one speaker from the range, and I have a pair of 'Super 8s'.
The 'Super 3s' have an efficiency of 91dB which is pretty good for a speaker of that size. The only problem is the bass will be limited.
If I wanted to do this, I'd use a pair of car speakers, which often have high efficiency (loud), but you have to check this. You want 90dB minimum, you can get 100dB which will sound twice as loud. Look for coaxial, round with a suspended tweeter. I'd get a pair of car radios, preferably identical, and an FM modulator, something like this:- http://dx.com/p/3-in-1-full-range-fm-transmitter-mp3-player-with-ir-remote-sd-mmc-mp3-usb-3-5mm-11218. Have a look on the site there used to be quite a few available, I can't be bothered to go through them all. You can probably get something like it locally, supermarkets here carry them. I'd put a 12V battery in each box and leave a slot for the radio. Tune the radios to the same channel, but wire up the speaker to the left channel out of one and the right channel out of the other. That's basically it.
Don't listen to the ragging about quality, FM stereo is remarkably good, it can be better than a vinyl LP, it just depends on the quality of the equipment.
Edited by wakibaki - 3/17/13 at 3:15pm