Ok I figured this out. Here is what I did for anyone who wants to know.
Installed Joomla using Script Installer into a subfolder of the site I wanted to update. Lets call this the Temp Install.
Script Installer creates a .script file within the domain id# folder which is located in this folder:
/etc/webmin/virtual-server/scriptlog
As Joe mentioned you can get the domain ID by typing into SSH terminal:
virtualmin list-domains --domain yourdomain.com --id-only
I backed this new .script file up.
I modified this file to match my install that I wanted to update.
The lines I modified were:
opts_db
You have to be careful to leave opts_db=mysql_ and just put your datebase name after that. i.e. opts_db=mysql_joomla
opts_dir
This is the absolute path to the install you want to update. No trailing slash.
desc
This is just the description but I removed the subfolder from it.
url
The URL to the install you want to update. Includes trailing slash.
user
The admin username to login to Joomla with.
opts_joomla_secret
This is the secret string found inside the configuration.php of the install you want to update. In configuration.php it is the line with var $secret at the start. Enter it into the .script file without quotes.
pass
The admin password to login to Joomla with.
version
I had to roll this number back to the actual version of the install. i.e. 1.5.9
opts_path
This must be / if your install is in the public_html folder (or httpdocs in my case). If your install is in a subfolder (i.e. http://www.yourdomain.com/subfolder) this would be set to /subfolder with no trailing slash.
Once I save this file overtop of the .script file that the Script Installer created and go back into the Script Installer within Virtualmin I am able to upgrade the install.
I can then either manually remove the Temp Install and database that I installed with the Script Installer
OR
I can have the Script Installer remove it by uploading the original .script file that the Script Installer created for the Temp Install. When it updated the install I wanted to update it renamed the .script file so it is then possible to simply reupload the original .script file and it shows up in the Script Installer. Just be sure it is the right one so you don’t remove your entire site.