I'm curious on how others handle one-click updates for themes and plugins not hosted on WordPress.org.
I use EDD's software licensing extension. It will generate a license key upon download/purchase. After activating, it will allow one-click updates on a customer site until the license key expires. It's designed to work with themes and plugins (at least in the context of WordPress products).
I haven't tested this one, but I've seen Reaktiv Remote Repo as a recommended solution. It only makes references to updating plugins, but I'm assuming it could be used for themes too.
There's a service called WP Updates that handles one-click updates for WordPress products, but I'm not sure if it's trustworthy anymore.
One I just got tipped off on by @turtlepod called f(x) Updater, which sounds like it's worth a look.
ThemeForest and CodeCanyon products can be updated with the Envato Market plugin.
Then there's this script, also untested by me. It's worth noting that it appears it was last updated over six years ago.
If you distribute themes and plugins outside of WordPress.org for whatever reason (probably because they're paid), how do you handle one-click updates?
As a follow up question, do you have any sort of mechanism to push "emergency" updates (like critical security fixes) without having to wait for the site owner to click an update button?