Under Tools, I inadvertently deleted a program from the Uninstall List ("Select a program from the list you want to remove from your computer"). How do I add the program back to this list?
The easiest way would probably be to reinstall CCleaner. I wouldn't uninstall your current version, I'd just reinstall right over the top of the current one. If that doesn't work you might have to uninstall, but I'd try it without uninstalling first. I don't know if that'll fix it but that's what I'd try first.
If you remove a program from the list, the only way to restore it is to re-install it (which restores the registry entry you removed)
Welcome to the forums (albeit many moons late.)