I'm trying to make a feature for a monk subclass that would make their Wisdom modifier to apply to their Persuasion and Deception checks, instead of their Charisma modifier. I know that the Hexblade Warlock has a feature that allows them to use Charisma when making attacks and calculating damage, but I haven't been able to find anything similar for ability checks. Anyone know how to do this? 

As far as I'm aware this isn't something that is normally done, in part because skills are already flexible. Persuasion may default to Charisma, but DMs can and do regularly call for skill checks with other ability scores as appropriate for the situation.

For example, Steath(Dexterity) could be for moving carefully through a dungeon, Stealth(Charisma) for moving through a crowd of people without drawing attention, or Stealth(Wisdom) for navigating around security cameras in a more modern campaign. Proficiency represents training, while the associated ability is just a best guess at what natural talent is likely to be needed.

Saying that a character can add their Wisdom to a skill check is perfectly reasonable (like unarmored defense), but replacing it might be a hard sell.

Sorry, maybe I'm not making myself clear. I'm saying I'd like to give them the option to use their Wisdom modifier instead of their Charisma modifier. It wouldn't keep them from still using their Charisma modifier if they wanted to. 

I get what you're saying that skills are already somewhat flexible, but for the feature I'm thinking of I would like it to be fairly explicit that the subclass can, if they choose to, use Wisdom for Deception or Persuasion instead of Charisma. 

My recommendation in this case personally would to actually take a look at the structure of a class from Pathfinder.

The Unchained Monk specifically. Alternatively, take a look at the elemental monk, or even design options similar to those of the Eldritch Invocations but for a monk.

Defined perhaps as training paths, and so on.

Take a look at those in specific if you have not already to perhaps get a better idea on how you would design the option(s).

If anything, I think the Eldritch Invocations are actually an excellent model for what you're looking to do, while the Elemental Monk can give you structure to work around without forcing you to do a full recreation and remodel of Invocations.

I'd also like to point, that previous editions of DnD have actually outright used a completely different base for saves, abilities and so on. Pathfinder having so many splat books, but it's also a precedent in 5e itself, where the base values are changed to a different attribute all together. Not a lot of split attribute focus going on.

What I mean is

Rangers are based are Wisdom

Paladins are based around Charisma

And so on.

So, overall if you wanted to make a change from what I under stand about your inquiry, you would theoretically need to change the base of the class to work around a different attribute, otherwise making a list of options for Monk Techniques and a more general school, while having the ability structure set similar to Invocations would be the alternative.

Absolver, which is a video game actually does this quite well.