Dealing with private, or non-repo updates myself recently, I've been exploring what it takes to do these. Currently I'm using Freemius, but I'm sure at some point I'll have to make this work. I'm excited to see another option out there!
We make it pretty easy to do with Kernl. It also supports "push to build" from GitHub or BitBucket if that interests you. If you have any questions send me an email: jack at kernl dot us