If they log into an account directly, you need to create a Google login for them (I'd suggest using the exact same username and password as you currently are) and make sure you check the box that's like 'other's may access this account'.
I have one client that logs in manually. He set up his own Google Account and invited me to be a manager. I previously had him linked to MCC. He is still linked their but the only difference is that I am not able to access Analytics. He has it set up but it does not show up when I enter through MCC.
Sorry for all the questions but this could be very tedious if I had to set up a Google Account for every client.
What have other people been doing that previously had all their clients linked to a MCC?
Your advertiser needs to send you the email request from that setting for you to have access to that information. Make sure they send it to your Google account MCC email address for a smooth process.