I get stones for tamer bags. I also get stones from wild battles. It's all RNG. To increase your wild pet battles per hour, you can pick a place with lots of spawns like the water wavelings for example. I usually go around the beasts of fable areas. Several wild pets. By the time I'm done, they are respawning. Don't really have to move. You will get a stone from the opening pet's family however, so these only work if you want beast, critter, or aquatic. I've got 4-5 beast ones this way as well as a generic Flawless
Hope this helps!