On a $50 budget it's going to be really tough to find anything, even with such a low power requirement. The Sure Electronics no_eye_dear mentions are one route, they sound decent and are pretty cheap, but not really DIY (just add case, power brick and you're done).
Another option might be TI TPA3123. It's a class-D chip that'll do 25Wx2 into 4R. Add a cheap 24V SMPS and some passives and you've got an amp. There's a schematic in the datasheet. These parts are supposed to sound decent. I still doubt you'd be able to do it for under $50 though, even if you etch your own boards.
LM1875 is probably doable - IF - you have a suitable transformer on hand. Otherwise the transformer alone will eat at least half your budget. It's easy to wire up on protoboard though and sounds great.
My advice is buy the Sure 15W module, wall wart, maybe a volume pot, and a cheap case for it. That'll consume your budget and it'll get you a decent sounding amp. Otherwise save more money and get a 41hz kit or build a chipamp.