Thanks for all the suggestions, guys, but I think you misunderstood the problem. The Pod::Coverage problem is not with my module; it's in the module that uses my module. I can't document the constant in my user's POD, I can't make the user declare it private and I can't force them not to use Pod::Coverage. I wouldn't even get very far advising them not to use it: there are all sorts of recommendations out there from very smart people telling them to do it, and Dist::Zilla even includes a Test::Pod::Coverage test in its release tests, if you turn that feature on.
tye's answer was 100% correct and solved my problem neatly and completely. ++ to him.
