I know there are options to disable chat totally or not to, but are there options to disable chat for certain users. Ideally I want a private chat within Teams meetings for certain members of that meeting that others cannot see. The options seem limited.
There's no such thing as "private chat within a meeting", meetings are a shared space. You can always create a separate chat with just the users in question. More generally speaking, if you want to restrict certain people from communicating with each other, take a look at the Information barriers feature.