Counters: Nihilego is one of the better ones. Loads of special bulk, resists both of Volcarona's STAB moves, and has Power Gem to scare Volcarona. It does have to watch out for a potential Hidden Power Ground or Psychic.
Heatran is also solid, immune to fire and 4x resists Bug, Ice, and Grass, and it can potentially grab a Flash Fire boost if Volcarona isn't careful. Like Nihilego, Heatran does have to watch out for Hidden Power Ground.
Gyarados resists fire and bug and has plenty of special bulk, it can fight back with Waterfall. It does have to watch out for Hidden Power Electric or potential burns (either Will-o-Wisp or Flame Body).
Mega Salamence resists fire, bug, ground, and grass and fights back with Hyper Voice or Double-Edge, but has to watch out for Hidden Power Ice.
Alolan Marowak resists fire, bug (4x), ice, grass, and electric (if Lightningrod), and OHKOs with Flare Blitz or Shadow Bone (Flare Blitz OHKOs max HP Volcarona, Shadow Bone only OHKOs offensive builds), but it has to avoid Hidden Power Ground.
Tapu Fini resists fire, bug, and ice, has plenty of bulk to take the odd Giga Drain or Hidden Power Electric, and can fight back with water moves.
Toxapex resists fire, bug, and ice, and can Haze Quiver Dance away. It doesn't like taking Psychic though, mostly because it has little offensive presence.
Volcarona can't run that many coverage moves, it's usually 2 STAB moves and 1 coverage move, with the final slot going to Quiver Dance, so it will always leave several openings offensively.