This is the plugin you want.

I’ve tried about 10 different methods (a mix of plugins and custom code) to achieve this task on a membership Android/iOS App that’s powered by WordPress. We use a custom login system from a third party database and that was causing conflicts with many of the “limit access” or “single login” plugins available.

I don’t know what’s different about this one, other than the fact it works, and it works great.