Nominating Machamp and either Pursuit Umbreon or Tyranitar.
Out of the most common Pokemon, Muk is likely to draw Tyranitar and Gengar into battle, the former being one of the safest opportunities to introduce Machamp, the later being susceptible to Pursuit.
Umbreon has the benefit of stopping most Curse users as well as mixed attackers, while it struggles against Misdreavus and does not contribute anything to the team's offense. Enforcing switches with Charm is great to get Muk/Machamp in undamaged.
Tyranitar provides Roar, but in spite of his stronger Pursuit, has a worse match-up versus Giga Drain Exeggutor and Dynamic Punch Gengar and adds further Nidoking problems, which Muk and Machamp already have.
Unlike Misdreavus, Exeggutor appears to be very common. It stops Machamp, is guaranteed to survive +1 Sludge Bomb at full health (assuming no poisoning and/or Hidden Power IVs) and can heavily damage Muk with Psychic.
+1 Muk Sludge Bomb vs. Exeggutor: 333-392 (84.7 - 99.7%) -- guaranteed 2HKO after Leftovers recovery
Exeggutor Psychic vs. Muk: 229-270 (55.4 - 65.3%) -- guaranteed 2HKO after Leftovers recovery
Therefore I think Umbreon is the better choice.
Machamp (M) @ Berserk Gene
- Cross Chop
- Curse
- Rock Slide
- Thief/Hidden Power Bug/Rest/Encore/Light Screen/Fire Blast (with Leftovers)
Umbreon (F) @ Leftovers
- Charm
- Pursuit
- Rest/Moonlight
- Sleep Talk/Toxic/Zap Cannon
The fourth moves are up to debate. Albeit gimmicky, Berserk Gene critical Cross Chop will kill a Starmie that has previously taken Pursuit damage.
+2 Machamp Cross Chop vs. Starmie on a critical hit: 286-337 (88.5 - 104.3%) -- 28.2% chance to OHKO