You can install Mambo on your account via the automatic script installation system - Fantastico. Here is the way of installing Mambo from Fantastico:

cPanel --> Fantastico --> Mambo --> New Installation

For detailed instructions on how to install Mambo on your account, please check this tutorial.

You can also request the script to be installed on your account by SiteGround Technical Support Team. They would gladly assist you with the installation of any of the script/application that are compatible with your hosting account.

Log in to your Customer Area --> Get Support Section --> HelpDesk --> Get script installed -> Script Installation