I can't add members to private channels!

I've figured out a direct solution to the issue, facing the same problem myself when we wanted to invite guest BETA testers to interact with and get feedback directly. The idea of deleting and re-adding the Team sounded ludicrous to me, so I kept trying to figure it out.

I was able to find a sequence that works consistently and is a direct solution to the problem you're all facing. I perform some of my steps in the Teams Desktop App and some in the Teams Admin Center. You'll need appropriate permissions, I'm a Global Admin for the domain. I'll post my steps in order:
Create a new Team in the Teams App. I created a Microsoft 365 Group for group email distribution, but I believe it will also work setup as a regular blank Team.
Once the Team appears in the App, create your custom "Private" Channel. 
Click on Manage Team and add a new Member. Enter the Guest's email address, and edit their display name prior to finalizing. Do this for all Guests. Remember, you're adding to the TEAM ONLY.
This is usually where adding the newly created user to the Channel fails.  Do not waste your time here any longer. Open the Teams Admin Center and navigate to the Channel itself. 
Teams Admin Center.
Teams.
Manage Team.
Click the Team name itself.
Click the Channels Tab.
Click the Channel Name.
Click the Add button.
Type in the guest user's Display Name.
Select and Apply.
Return back to the Teams App, within a few seconds you should be able to verify that the Guest is a Member of both the Team and the Private Channel.
You're done.
This should work consistently; I've used this method on three Teams and across 6 Private Channels now. Good luck everyone!