Sap sipper azumarill turns a weakness to an immunity. Use that as its main selling point. It works wonders on defensive sets especially perish song. Bulky sets become even more likeable with that new fairy type making able to take 0 damage from specs d-meteor latios.
Okay, you get to switch into Grass moves with impunity. Woohoo, you prevent Breloom and Smeargle from using Spore and other 'Mons from Grass-moves.
In fact, Breloom is walled, congratulations. Too bad Azumarill does not have a Recovery move outside Aqua Ring (lol) and Rest to use to try to stay relatively healthy. Chip damage can add up.
Spore immunity does not stop Smeargle from laying down entry hazards, though. Smeargle's Focus Sash had better be broken, or else you're looking at a 2HKO, regardless of your now pitiful attack. If Smeargle somehow took some light damage, such as switching into Stealth Rocks once, you'd need Super Power to OHKO, assuming no attack investment since you're presumably investing in Azumarill's defenses.
But to do what? Set up Light Screen? Fish for a Sing? Toxic? Encore? Knock Off? Perish Song? Perish Song is a dicey concept to begin with. Admittedly, Mega-Gengar could pull it off, and I also had some success with Hydration Lapras, Prankster Murkrow, and Misdrevous in Pokemon Black/White. For Azumarill to pull off a trapper set has to trap with Whirlpool, pull off a Perish Song, and try to survive until then. 100/80/80 is pretty bulky, but there are definitely 'Mons that can 2HKO or even OHKO it, rendering the strategy moot. There is also the aforementioned problem of staying alive. U-turn and Volt Switch only compounds the problem of trapping.
Oh? You only want to use Perish Song to force a switch? A threatening check/revenge killer in Huge Power Azumarill has more general utility than a sitting duck Sap Sipper Azumarill that forces a switch every three turns it is sent in. You want a Perish Song user that is immune to various Grass Moves in a Stall Team? Use Celebi. It's not immune to Giga Drain, Energy Ball, Powerwhip, etc, but I am sure it can comfortably take a couple with its 100/100/100 defenses, especially when combined with Recover. It can't wall every dragon, but there are six slots for a team here.
It is not like you stop that hilarious Substitute/Protect/Leech Seed/Curse Trevanent set just because it cannot use Leech Seed. It is not like you stop Mega-Venusaur from Sludge Bombing just because it cannot use Grass-moves.
I get that you do not want to be a 'generic blue egg' but sometimes a particular Pokemon trait/set is favored for a good reason.
Keep in mind that it is not like you have to stop using Sap Sipper Azumarill just because of this wall of text. You should feel free to use whatever you want. c:
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Back on-topic: the curse sets that pkmn-taicho321 and Yamborski suggested both seem interesting. I might try them out sometime soon...