I have a private application that will be installed in about 500 to 1000 phones. I'm concerned about how I'm going to update all of those. I don't want to list it on Google Play (since it's a private app). I've also read this question but it involves me firing up a server for this.
Is there any online alternative that I can send my updates to and they distribute it to my devices?
Try Hockeyapp: https://www.hockeyapp.net/features/
It's free for 2 apps.
Absolutely agree with Katharina's reply. I just want to explain in more detail about HockeyApp.
HockeyApp is a platform used to test apps for developers. Every account automatically comes with our free plan, which offers unlimited distribution, crash reporting, and feedback for 2 apps – allowing you to get started and explore without any monetary commitment.
The most important step is to integrate a HA SDK speficied for your platform, for your case, it should be Android https://rink.io/sEptDQM. Then you could benefit from following HA features:
If you have any questions, please contact us at support@hockeyapp.net