In the entire time that I've been battling (since launch, and my Jade Tentacle
will attest to how much time I've invested), I have only gotten one battle stone from a battle, ever. It was from a Stunted Yeti. As for some of the pets listed in a previous post, I rarely see Cogblade Raptors, maybe fought a grand total of 5 of those, just trying to upgrade my Common. Oily Slimelings are rarely up when I go there. Kun-Lai Runts, however, I do see a lot of, but now I have a Rare, and won't care any more.
So, TL;DR version: I farm Trainer bags.