Dark type's supernatural matchups don't make sense as they are merely mean animals.

It could have been a sort of "goblin" type. A reverse Fairy type, with low special and high physical stats. Including creatures that are either beastly or shifty demons, but.....it just includes mean Normal types.

So to create the least mess possible, just remove its immunity to PSYCHIC and its effectiveness against GHOST.

>But then Ghost only has one weakness!

How about we solve two issues at once? Fairy does not interact with Psychic and Ghost which is rather weird.
So how about this triangle:
Psychic
Ghost Fairy
>clockwise, with Psychic beating Fairy, as it is supposedly a superior type, like dragon.