I'd suggest finding another way to deal with ferro, as superpowers drops are rather costly especially to cover just two pokemon - ferrothorn and empoleon being the only two fully evolved pokemon that resist Water and Fairy (unless I've missed an ability on something else), as a neutral +6 waterfall from Azu will kill most everything anyway.
While that could work as a check, just like Meteor said, a better one to shut Azumarill down would be Sableye. Prankster is an amazing ability and all you have to do is Taunt Azumarill so it can't Belly Drum, then use the status move of your choice to cripple is for the rest of the match.
I don't know what Sableye is running but here's how I see it assuming the worst (252HP/252+Def):
First off, we can eliminate the possibility of anyone switching BD Azumarill into Sableye because that's stupid.
So,
Switching Sableye into Azumarill:
If you switch sableye in then they're probably drumming or have drummed already if you're revenging or whatever, in which case you're probably going to have to take a +6 aqua jet unless sableye now runs speed investment, and while it's not a guaranteed KO without prior damage or mysticwater, it's still not pretty:
+6 252+ Atk Huge Power Azumarill Aqua Jet vs. 252 HP / 252+ Def Sableye: 274-324 (90.13 - 106.57%) -- 43.75% chance to OHKO
If you're not running a defense nature then:
+6 252+ Atk Huge Power Azumarill Aqua Jet vs. 252 HP / 252 Def Sableye: 301-355 (99.01 - 116.77%) -- 93.75% chance to OHKO
If you outspeed and WoW them:
+5 252+ Atk Huge Power Azumarill Aqua Jet vs. 252 HP / 252+ Def Sableye: 240-283 (78.94 - 93.09%) -- guaranteed 2HKO
If you do that and they have mysticwater:
+5 252+ Atk Mystic Water Huge Power Azumarill Aqua Jet vs. 252 HP / 252+ Def Sableye: 288-340 (94.73 - 111.84%) -- 68.75% chance to OHKO
EDIT: Ooops burn halves, see Martingale's post below. Other calcs have been replaced with corrected versions.
So sending in Sableye is generally not a good idea if Azumarill has drummed or can drum on the switch. It might work against a leftovers/sitrus one with no speed investment, but even then you're going to sacrifice sableye without even taking it out.
Predicting the Switch, which I assume is what you're talking about because you mention priority Taunt:
If you predict a switchin and switch in sableye at the same time, and you taunt them, and they for whatever reason don't switch out in fear of status (perhaps carrying Lum), then I doubt they're also going to be unaware of prankster Taunt, so they'll attack. If you Taunt and they do this, you're dead:
252+ Atk Huge Power Azumarill (Move 1) vs. 252 HP / 252+ Def Sableye: 308-366 (101.31 - 120.39%) -- guaranteed OHKO
That's with azumarill set as water/fighting using a 90bp fighting move on a dark-only sableye, to emulate STAB play rough hitting for SE damage.
So your best bet in this case is to go with priority WoW and hope that they for some reason left a non Lum Berry Azumarill in on something with priority status:
252+ Atk Huge Power burned Azumarill (Move 1) vs. 252 HP / 252+ Def Sableye: 154-183 (50.65 - 60.19%) -- 85.94% chance to 2HKO, Aqua Jet: 11.18 - 13.48%
Neutral unboosted Aqua jet deals 22.69 - 26.97% to max hp/def sableye, so I guess this works given lefties and no prior damage, but you're relying on non-Lum Azumarill staying in on something that carries priority WoW, which is kinda dumb for someone to do.
Also if you mispredict the set and they're running choice band:
252+ Atk Choice Band Huge Power burned Azumarill (Move 1) vs. 252 HP / 252+ Def Sableye: 232-274 (76.31 - 90.13%) -- guaranteed 2HKO
Basically, you reduce the threat it poses (though even burnt +6 is still very serious power) and make it easier to kill as a result, but are probably going to lose sableye in the process.
Maybe I've missed something but generally speaking it's not looking that good unless your opponent doesn't know what they're doing and/or you can predict real well, and Sableye is running Max HP/Def with a +Def Nature. Even then it doesn't work out like you've said, so help me out here?
As I see it the best way to handle BD Azu is to prevent it from belly drumming in the first place, generally by dealing enough damage that it can't (and the fact sitrus helps reduce the number of things that can do this to it is part of why I like it so much), seeing as it can stand most statuses that aren't sleep (which most people relying on BD Azu for sweeping should have something to absorb anyway). Otherwise, revenging it with something that can take a +6 Aqua Jet (or waterfall/play rough if slower) or something faster with strong enough priority is the best way to deal with it.