This might put me in the minority here, but honestly, I hope that Zoro doesn't awaken Conqueror's Haki, nor any of the other Straw Hats, either. And this is coming from someone whose two favorite characters in the series are Luffy and Zoro, and Sanji is tied for my number three spot. At least hear me out on this, even if you disagree.
Conqueror's Haki was introduced as a big deal for someone to have, a "one-in-a-million" chance that people are born with. If Zoro awakens Conqueror's Haki and Sanji does not, that would put Zoro and Luffy way too far above Sanji (who is already slightly below Zoro as is) in terms of strength and would really make it into more of a Monster Duo. But, if Sanji does get Conqueror's Haki, too, then we would have three Straw Hats who could use it. Hardly "one-in-a-million"; to be honest, it would be really difficult to swallow that three people with Conqueror's Haki would end up on the same ship. I don't like it when series do that: when they introduce some strong, special ability that only a few people are supposed to have, only to later say "LOL JK a lot of people can actually use it". If Zoro and Sanji–or even just Zoro--who are Luffy's top subordinates, get CoC because they're "really strong" members of the Straw Hats, then hell, why doesn't any really strong person get it? The Fleet Admirals, the regular Admirals, all the Warlords, all the Emperors, their top subordinates…you can't have it both ways. Either Conqueror's Haki isn't actually rare and any very strong person should be able to awaken it (and in that case, various characters should not have acted nearly as shocked as they did when they saw Luffy and others using it), or it truly is rare and even some of the very strongest don't get it.
Not only that, but Luffy being the only one with Conqueror's Haki in the Monster Trio/the entire crew is a good way to ultimately set him above the rest and reassert that yes, he is indeed the leader. Zoro and Sanji (Zoro in particular) already aren't that far below Luffy strength-wise. It's been pretty heavily implied that all three of them can use both Armament and Observation Haki. If they got Conqueror's Haki, too, would they really be below Luffy strength-wise? Especially Zoro, who can apparently cut through anything and hasn't even been challenged post-timeskip. I always thought that Zoro's insanely strong bloodlust and killing intent (usually stronger than Luffy's, actually) was a perfect substitute anyway. It's not real Conqueror's Haki, so it won't knock out the weak, but it will freak them out and cause them to freeze with fear. I'd say a captain with Devil Fruit powers and all three types of Haki and a Number Two with two types of Haki, a pseudo-third type, and some of the best sword skills in the world is a stable combination.