There are a lot of companies popping up, creating membership-based private rss feeds for podcasters. Memberful, Supercasters, supportingcast, etc... I believe it is already possible to use this plugin to set-up private rss feeds, tho it's not built into the UI for that purpose. Tho honestly, I'm not 100% sure what consistutes a "private feed," - other than perhaps, simply an unpublished feed?
There are no wordpress plugins built for this purpose, other than those supplied by a third-party membership services (mentioned above), and all are very expensive (~$300/year). The only benefit of these services is they offer a way for their members to quickly launch their private feed into any podcast player. Again, this may be possible thru this player using the call to action links, tho I am not 100% on that functionality. Anyway, sorry for rambling, but I just wanted to point out the potential.
Im not very familiar with private feeds, but you hide the RSS feed URL from the bot/search engine so it become kind of private. Perhaps use the plugin Yoast SEO to block the feed from bots.
Max from the Sonaar.io Crew
You guys should seriously look into it. If I had a way to generate individual private rss feeds to give to my site members, it would be killer. Currently no other plugin on wordpress makes it simple to create private rss feeds for podcasts, and it's about to be the next big thing. Apple started it on their platform, Spotify is testing it on megaphone and already live with it multi-platform thru anchor. Every membership platform is incorporating private rss feeds for bonus content. If that functionality was built into the podcast features of this app, it would be KILLER! It's something a lot of people are looking for at this moment. Look at Supercasters, Memberful, Patreon, etc.
As much as I would love to help you, this feature is not possible with Sonaar at the moment, beside the fact that you can generate a RSS feed and keep it hidden from the public/search engine.
On my end, I tagged this ticket as a feature request so that our development team can consider this option, but this doesn't guarantee that Sonaar will indeed implement this feature.