I once tried to replace the battery of my old iPod Mini (Gen2?). While I managed to replace it, I also managed to ruin the entire casing with ugly screwdriver scretches. I wouldn't want to see my Kindle end the same way...
On the other hand, the $59 battery replacement offered by Amazon for the Kindle 2 doesn't sound like a bad deal. It's comparable to what you would pay for
fixing an iPod device.