I'm trying to automate WHM to download and install Joomla into any new cPanel accounts I create, rather than doing it manually each time. However I can't find any permalink to the latest version of Joomla that I can use to grab the required zip. Does one exist?
Sadly unlike WordPress and other content managements Joomla as far as I know have opted not to use
Your best bet would be to subscribe to Joomla's RSS feed at http://feeds.joomla.org/JoomlaSecurityNews and look out for new updates then login to your administrator panel and do the click update.
WordPress now auto updates...
It's worth mentioning that WordPress as of 3.7.1 includes a automated and unattended update feature, maybe Joomla will follow suit.
For Long Term Support (LTS) branch -( Recommended) Stable release
Short term support (STS) branch
All these XML files have link to their details zip files.
You have to look at the last node of each XML file for getting latest version.
Hope it helps..