This matchup is in Slayer's favor.
However, Zappa is a unique character and you'll have to know your way around to avoid getting zoned by certain summons. Zappa has 5 possible states: naked, dog, sword, ghosts, and Raou.
Vs. Naked Zappa
-This is the form that you must take advantage of, similar to A.B.A. in non-mohora mode.
-Watch closely for his summon and play very conservatively - note that Dandy moves if executed to slowly or too closely will be punished by the summon. In short: stay out of point-blank range.
-Zappa has few ways to punish Slayer's lows, so keep at simple pokes (5K, 2H, 2K, 2S, 6P) and keep landing knockdowns so he can't summon.
-6K okizeme, if executed too slowly, can be punished by reversal summon.
-OVERALL: Play it safe and force Zappa to summon without hitting you. Letting him have orbs is a no-no. It's often smart to burst if he hits you with a 2D to deny him the orbs from the summon.
Vs. dog
-This is a problem if you aren't patient. The dog is an excellent zoning tool and if not played against correctly will have you eating way too much damage.
-Do not recklessly dash/jump/iad at Zappa, he dog's anti-air hits an extremely large area.
-Whenever the dog is within 2P range, spam it. This is the most effective way to kill the dog.
-Don't use any moves with lots of recovery (such as BBU), because the dog will eat the hit and Zappa will have free reign to punish you.
-OVERALL: Play it safe and poke the dog when the opportunity rises.
Vs. ghosts
-In my opinion, this matchup is just as hard as the dog.
-Watch for the backdashing mixup, the exploding ghosts WILL beat out your AA moves.
-Most Zappa players will zone you to death with these - the key is to learn to block well and slowly advance forward.
-If the Zappa player tries to go more offensive, watch his air motion and 2S accordingly. Otherwise, watch for his landing and throw him afterwards.
-OVERALL: Play defensively! You WILL get zoned, but rushing in will get you punished!
Vs. sword
-Not as hard as the other summons because he can't zone you as well with a sword.
-Zappa's 5HS with sword eats a lot of Slayer's pokes, so be careful.
-You can BBU after the sword rush attack.
-OVERALL: Not as hard, watch for long-ranged pokes, try to punish the slower attacks.
Vs. Raou
-This is my own particular experience against Raou; most others prefer to play extremely defensively, but I differ.
-Raou makes most Zappa players feel like they're in control. In reality, Raou can be punished quite easily.
-Blocking against Raou eats a lot of chip damage and opens up room for mistakes (such as getting hit by the deceptive looking dust).
-Your priority is still superior in many cases, try to go for knockdowns and throws - run the Raou timer out!
-Watch for Dark Anthem (super) and DoT it on reaction for the win.
-OVERALL: This is a tossup. You can play defensively if you want to, but be very good at blocking. In my opinion, Raou can be punished because Slayer's priority is still higher...so take advantage of that.
OVERALL
This matchup is definitely in Slayer's favor. The main thing that you will lose to would be careless mistakes and doing unsafe moves that lead to getting hit by summon or getting zoned. Lows are amazing in this matchup, especially 2H and 2D. Keep him at a desired distance and don't let him hit you with summon.
I'm sure you guys have a lot to add, I sorta just threw this together rather quickly. Post below and I'll add to the list.