I need an Everstone because I don't want my Torracat to evolve. I've been meaning to ask this question a while ago, but I forgot and and at one point the computer wasn't working, etc.
You can be given an Everstone by Ilima after you defeat her in Post-Game. You can also find one at Poké Pelago's Isle Aphun by doing the "Path for Brilliant-Stone Hunting!" expedition.
If you have a Pokémon with Thief/Covet, you can "steal" an Everstone from Roggenrola in Ten Carat Hill.