I replaced the battery on one of my Paperwhite's a year ago and the replacement battery wasn't any better than the old one. It had to be charged every day. I got a cheap battery from Ebay instead of getting what I've been told is a reliable battery from Newpower99. I've never actually used one of their batteries but I've been told they're good.
Here's a link to the battery for the 2nd generation Kindle:
https://www.newpower99.com/SearchRes...x=0&Search.y=0
Barry