Well since a gold farmer decided to update this thread, so will I.
It really depends on the type of Zappa you play against. Most will, however, use vomit a lot and/or dash up summon. So in this sense, using S.Ball or S.P formation or K.Ball j.HS are all great ways for stopping that annoying stuff. Since Zappa has no real fattie combos, you can almost always save your burst for either gold or to deny a summon (the latter is more common for me).
Sword: it depends how good your Zappa's spacing is. If he uses Sword Rush recklessly, you can punish the followup with a 2S (or even the Sword Rush itself if they're too close). Learn to bait the sword DP, though it hits pretty high up so be careful with your double jumps and back air dashes.
Dog: Run away, don't fall into a corner. What you can do to get away is TK Ball Seisei and use that velocity to move you upwards then airdash away while summoning more air Ball Seiseis, thus carrying you across the stage effectively. From then on you can just spam balls from full screen and try to avoid getting counterhit.
Ghosts: Pretty annoying. The ghost projectiles make it difficult for you to freely summon. You're going to have to wait for opportunity (ie. when all ghosts are used up) to try and rush him down. Aim for any far poke, honestly, or summon balls and start hitting them asap. Otherwise, be mindful of your surroundings if you're haunted - banana peels, pebbles, flower pots zoning reminds me of Arakune except I can actually win this matchup
Raou: People say run away, but I say fuck that. Of course play safe, don't walk into DP, and block his 5D, but going for long attack strings / block strings and quick knockdowns is a great way of putting pressure on Zappa.
Be extremely mindful of spacing in this matchup. Zappa has a quick, low dash that will often score him free summons if you're not careful. Don't force yourself on him - go ahead and spend the match running away and safely poking/summoning. This method will also help you avoid being hit by vomit. Staying airborne is OK in this matchup because he has few ways of taking you down without having a summon out first. Even then, it's a great way to bait anti-airs and scoring a knockdown. I would only go for heavy lockdown if the Zappa is scared and bad at reversals(which is probably none of them).