Managed Google Play also allows developers to publish private applications for certain managed Google Play enteprises (up to 20 enterprises per app). This can be done by whitelisting managed Google Play enterprise ID by the application developer.
First, discover your managed Google Play enterprise ID by going to Infrastructure diagram and check Managed Google Play Enterprise item.
Contact application developer to whitelist the application for this managed Google Play enteprise in their Google Play developer console, section Store Presence - Pricing and Distribution.
They have to select Choose organizations and enter this enterprise ID in the popup.
After the developer has whitelisted the domain, enterprise admin must approve the application for their managed Google Play Enterprise. For more information about approving applications, see How to add managed Google Play applications.
Rest of the application deployment workflow is similar than public applications.