I use Calibre for managing eBooks that I have got from outside the Amazon Kindle store, and for backing up the books I have bought from Amazon. It has always irritated me that it does not autoupdate, and the update process involves downloading a DMG and copying from there. I finally got annoyed enough with it to do something.
Below is a Gist that I’ve written that acts as an updater script. It is a bit rough round the edges but appears to do the job at least. This will check if a new version is available, and if so download it, mount it, update the application, then unmount the DMG. Any feedback is welcome (bash scripting is not one of my strengths).