An email address can only be used to own one account in eagle.io (including managed accounts). For example, my email address already owns one account in eagle.io, so if I try to create a new managed account with the same email address, I get this message:
However, you can use a different email (such as a personal Gmail account) when creating a managed account, and you won't actually need to use that email when logging in to eagle.io. That's because the owner and all the admins of the parent account automatically become admins of each managed account. So the regular credentials that you use for your main account will work fine for all managed accounts.
You can even use the same Gmail address to sign up for multiple accounts, by appending a plus and extra characters as explained in this blog post: https://gmail.googleblog.com/2008/03/2-hidden-ways-to-get-more-from-your.html