Counter That Core!

First off, I'm pretty sure your Azumarill set is missing the move Belly Drum.

Spoiler: Reborn's Core

Venusaur-Mega @ Venusaurite
Ability: Thick Fat
EVs: 248 HP / 96 Def / 144 SpD / 20 Spe
Bold Nature
- Giga Drain
- Sludge Bomb
- Synthesis
- Hidden Power [Fire]


Conkeldurr @ Assault Vest
Ability: Guts
EVs: 252 Atk / 236 SpD / 20 Spe
Adamant Nature
- Drain Punch
- Mach Punch
- Knock Off
- Poison Jab


Tyranitar @ Choice Scarf
Ability: Sand Stream
EVs: 252 Atk / 4 SpD / 252 Spe
Jolly Nature
- Pursuit
- Stone Edge
- Crunch
- Superpower
While this core is completely theorymonned and hasn't been tested, it seems to be fairly solid and doesn't have a bad time against your core. Looking at the original core, Belly Drum Azumarill is always scary, so I thought I would start with a strong answer to it, Mega Venusaur. Mega Venusaur is a strong answer to Azumarill and Mega Sceptile, only being 3HKOd by Mega Sceptile and OHKOing in return and being able to take any attack from full at +6 after rocks from Azumarill and OHKOing in return after a belly drum. Outside of the provided core, Venusaur can switch in to things like Breloom, Scizor and Ferrothorn, things that the rest of the core can struggle with. However, it is countered by Heatran. This is where Conkeldurr comes in. Conkeldurr is able to eat up multiple Fire Blasts from Heatran and have a good chance of OHKOing after stealth rocks, picking up the KO with Mach punch the next turn otherwise. Conkeldurr also has a good matchup against Mega Sceptile, being able to eat up any attack and KO in return with Drain Punch + Mach Punch. Conkeldurr also beats Kyurem-B, which otherwise can fire off super-effective Ice beams against Venusaur. Poison Jab is used as an additional coverage move to deal with Azumarill and other Fairies, while Knock off is to punish switch ins. Both of these Pokémon struggle with birds and psychic types, so Scarf Tar is an obvious partner. Tyranitar is able to pursuit trap the Lati twins and other psychic types and counters standard Talonflames. As both of the above core members lure in these Pokémon, clever doubles can eliminate these Pokémon from the battle. Tyranitar is also able to outspeed and KO Heatran after some prior damage.

The core does outright get beaten by Mega Alakazam, and does appreciate having hazard both removed from your side and on your opponent's side. Because of this, Pokémon like Talonflame which can KO it with priority Brave Bird and Mandibuzz which removes hazards and beats Mega Alakazam make for great partners to this core. The core also has an uncovered steel weakness

Calcs:

Spoiler

252 SpA Mega Sceptile Dragon Pulse vs. 248 HP / 144 SpD Mega Venusaur: 115-136 (31.6 - 37.4%) -- guaranteed 3HKO after Stealth Rock
0 SpA Mega Venusaur Sludge Bomb vs. 0 HP / 0 SpD Mega Sceptile: 264-312 (93.9 - 111%) -- 62.5% chance to OHKO

+6 252+ Atk Huge Power Azumarill Play Rough vs. 248 HP / 96+ Def Mega Venusaur: 250-295 (68.8 - 81.2%) -- guaranteed 2HKO after Stealth Rock
0 SpA Mega Venusaur Sludge Bomb vs. 92 HP / 0 SpD Azumarill: 278-330 (76.3 - 90.6%) -- guaranteed 2HKO

252 SpA Heatran Fire Blast vs. 0 HP / 236 SpD Assault Vest Conkeldurr: 127-150 (36.1 - 42.7%) -- guaranteed 3HKO
252+ Atk Conkeldurr Drain Punch vs. 0 HP / 4 Def Heatran: 270-320 (83.5 - 99%) -- 75% chance to OHKO after Stealth Rock

252 SpA Mega Sceptile Leaf Storm vs. 0 HP / 236 SpD Assault Vest Conkeldurr: 162-192 (46.1 - 54.7%) -- 58.6% chance to 2HKO
252+ Atk Conkeldurr Drain Punch vs. 0 HP / 4 Def Mega Sceptile: 180-213 (64 - 75.8%) -- guaranteed 2HKO after Stealth Rock
252+ Atk Conkeldurr Mach Punch vs. 0 HP / 4 Def Mega Sceptile: 96-114 (34.1 - 40.5%) -- guaranteed 3HKO after Stealth Rock

252 SpA Heatran Flash Cannon vs. 0 HP / 0 SpD Tyranitar in Sand: 176-210 (51.6 - 61.5%) -- guaranteed 2HKO after Stealth Rock
252 Atk Tyranitar Superpower vs. 0 HP / 4 Def Heatran: 254-300 (78.6 - 92.8%) -- 37.5% chance to OHKO after Stealth Rock

 

Infernape's Core

Spoiler

Politoed @ Damp Rock
Ability: Drizzle
EVs: 248 HP / 164 SpD / 96 Spe
Calm Nature
- Scald
- Toxic
- Encore
- Rest

Sableye @Leftovers
Ability: Prankster
EV's 88 HP/ 252 Def/ 168 SpD
Relaxed Nature
Moves
-Foul Play
-Taunt
-Recover
-Will O' Wisp

Kyurem-Black @ Life Orb
Ability: Teravolt
EVs: 20 Atk / 252 SpA / 236 Spe
Mild Nature
- Ice Beam
- Earth Power
- Fusion Bolt
- Roost

Spoiler: Explain!

Now, as opposed to going for a more offensive route, I'm going with a more defensive route Now let's start with Politoed. Politoed is used to shut down Heatran because c'mon let's be honest. Heatran cannot do diddly squat to Politoed while rain is up. Next is Sableye, Sableye is just used to screw up stuff but especially Azumarill. Will O' Wisp that thing and it is worthless, even with a Belly Drum up. Kyurem is just the clean up crew. An Ice Beam for Sceptile, a Fusion Bolt for Azumarill and an Earth Power (if Politoed didn't take care of him already) for Heatran after the Air Balloon is broken.