I can picture this being Psychic/Dark, unless you have another combo in mind.
Here's an ideal move I came up with for it.
Name: Dark Beam
The user shoots a beam of black magic towards the enemy. It can cause the enemy to flinch. It is also super-effective on Fighting Types.
I came up with the bonus effect after knowing the new move "Freeze Dry" is confirmed to be super-effective on Water Types.