Flame Burst
Leaf Storm
Smelling Salts
Wish
One thing I want to point out is how CAP24 does NOT fit in with the rest of the Pokemon in the Fairy Egg Group.
Check out the list on Bulbapedia. Slurpuff looks the most similar to CAP 24, but CAP24 is at LEAST 100 times heavier with the competitive weight minimum of 500kg. Excluding the outlier Glalie, CAP24 is also at least 10 times heavier than pretty much all of the Pokemon in the Fairy Egg Group. Basically, these Pokemon are generally really light, and CAP24 is not.
The Grass Egg Group felt natural for CAP24. Human-like seemed appropriate, but then I realized that CAP24 has 4 legs. Luckily, quite a few Monster Egg Group Pokemon are quadruped.
On to actual moves. Flame Burst didn't feel like it fit in the level-up movepool, so it's here. Leaf Storm fell into here because I wanted Solar Beam in the level-up pool. Smelling Salts can be learned by chain-breeding, originating from Hariyama. I didn't find a good place to fit Wish in the level up pool, so it's here.
Gen 7 Pokemon have very small Egg Move pools, so I'm capping it on four here.