Looks like someone has suggested a pull request for Avogadro 1.x with AppImage support:
Since it relies on Travis builds, I’ll see if we can get this ported to avogadrolibs as well.
If there’s anything I can do to aid in this, please do ask. For example, I’ll be happy to try out the AppImages you build in my various virtual machines and Linux installs (I have ~10 distros installed to my hard disk, and an additional 20 installed in virtual machines).