Is there a way to publish an app to a store as "unlisted"?

I would like to publish an app that is not yet ready for the public, but at the same time allow a few select people to beta test it, and I would like to use the play store rather than sending .apk files around due to it being able to auto-update the app easily.

Is there a way to do this? if not on the play store, on another store (Amazon?) - if still no, what would be the best way to proceed?