I just upgraded the battery in one of my DS4 controllers with one of these.
http://www.amazon.com/gp/product/B004I8II22/?tag=neogaf0e-20
So far so good, and definitely seems to be a significant battery life improvement. I used my controller that had a creaking left palm rest as the guinea pig, and now it doesn't creak anymore, so maybe tightening the screws fixed it or something about the slightly larger battery inside.
It does not fit in the battery plate as it is slightly bigger than the original. However, I sat it roughly on the same spot and closed the thing up without securing it via tape or anything, and it doesn't seem to be loose at all or anything within the controller.
Main things to watch out for if you do this upgrade - 1) try not to let the triggers come off when removing the back plate, as you may lose a spring this way. They are tiny and easy to lose. There are plenty of vids on YouTube about this already. 2) There's a little rubber stand that sits on a part of the battery plate that's also easy to lose (and can take a few minutes to figure out where it goes if it does come off and you've never seen the innards before). 3) The battery cables are longer than what is present on the original battery. Take care not to get them caught between the front and back plates when reassembling your DS4.