Did a quick search on eBay and your options are really limited. Found a 250W supply, which would safely handle the 6570, but it's ludicrously expensive at $105. My top of the line, SeaSonic X650 Gold (one of the best 650W PSUs on the planet) barely cost that much. Managed to find the same PSU on another site for $80, but that's still grossly overpriced.
Looks like people are exploiting people like you who are just trying to get a bit more life out of old computers by gouging on the PSU. These PSUs should cost, at most, a third of what they're asking, probably less. 250W supplies are dirt cheap.
The only way I could see you getting a new PSU for any kind of reasonable price would require that you leave the side panel off the case and just lay the PSU on top of it. All PSUs, even these crappy oddly shaped ones like you need, use the same connectors and produce the same voltages. Almost any old PSU will plug into your motherboard and power it, the question is only of whether or not you can actually attach it to your case, which isn't strictly necessary.
But again, this is not something I'd really recommend doing. It's unsightly, and if you're careless and bump into the case while the PSU is perched precariously, it could fall into the case and cause permanent damage to your motherboard. Your computer will also be louder, may run hotter (just as likely to run cooler actually), will collect more dust, and if you have a cat...