This feature does not work on macOS Sierra and higher because of "Gatekeeper Path Randomization", also known as "app translocation" and may be removed from Tunnelblick in the future.
You can distribute Tunnelblick with configurations that will be installed automatically when Tunnelblick itself is installed. This does not require rebranding and uses a standard, digitally-signed Tunnelblick.app, however, it cannot update configurations the way that a Deployed version can.
When Tunnelblick installs itself, it looks for configurations to install in the "auto-install" and ".auto-install" folders that are in the same location as Tunnelblick.app.
The "YOURNAME" folder now contains the following:
The auto-install (or .autoinstall) folder contains your configurations, perhaps in subfolders
Finally, create a .zip of the "YOURNAME" folder by control-clicking the "YOURNAME folder and clicking on "Compress YOURNAME". A "YOURNAME.zip" file will be created.
That "YOURNAME.zip" file is what users should download.
(Or you can create a .dmg that contains the contents of the "YOURNAME" folder. That's more complicated and not explained here.)
After downloading "YOURNAME.zip", users may need to double-click the .zip file to expand it (their browser may do that automatically).
A Finder window will appear with two items: Tunnelblick.app and a folder named "autoinstall". To start the process, they need only double-click Tunnelblick.app.
After finishing the installation, they may discard the "YOURNAME" folder and/or the "YOURNAME.zip" file if they wish.