Neither Ghost nor Dark should resist Fairy. It might be nice for one to resist and the other to be weak to Fairy, but then Sableye/Spiritomb will still have no weaknesses(which is kind of an issue). Between Ghost and Dark, Ghost should be weak to Fairy given the two immunities and two resistances while dark is immune to one and resists itself and ghost(If poison were to gain use, Ghost would be more useful resisting both Poison and Fighting whereas Dark is weak to fighting). I wouldn't give Dark another advantage given the immunity and the fact that it only has two weaknesses. Psychic is only SE on Poison and Fighting, has no immunities, and has three weaknesses, so Fairy SE on Ghost but Dark and Fairy(imo) should share a neutral relationship. I think Flying is fine, but I do believe GameFreak needs to introduce a much wider variety of moves for other types to abuse.
To add to type chart predictions(Kind fun I must admit):
Fairy
Supereffective: Dragon, Fighting, Ghost
Not Very effective: Ice, Fire
Resists: Dragon, Fighting, Ghost
Is weak to: Poison, Steel
Amendments(if they were to happen):
Ice
Resists: Fairy, Ground, Ice, and Water
Grass
Resists: Rock, water, grass, and ground