The Thylacoleo (Marsupial Lion) is a carniverous marsupial that lived between 1,6000,000 - 40,000 years ago. It was 1.5 meters long from head to tail and 75cm tall at the shoulders. The Marsupial lion was the largest meat-eating mammal to have lived in Australia, and one of the largest marsupial carnivores the world has ever seen. It would have hunted animals including the giant Diprotodon in the forests, woodlands, shrublands and river valleys.
The Marsupial lion had enormous slicing cheek tooth, large stabbing incisor teeth at the front of the mouth and a huge thumb claw. The claw may have been used to disembowl it's prey or hold down stuggling animals.
Another possibility is the Tasmanian Tiger that has been thought to be extince since 1932. This is the Thylacine which was variously called Tasmanian Tiger and Tasmanian Wolf. It, too, is a marsupial.
Thylacine cyanocephaplus
The Jaws that bite...
The last living pair... now deceased... or are they?
Cryptozoology is such fun!
I recently read somewhere that there have been many seemingly reliable reported sightings of the Tasmanian tiger throughout Australia and even New Guinea. Someone is mounting an expedition to look for it.
Regarding mountain lions, a friend of mine spotted one in a park in Jefferson, New Jersey (no more than 50 miles northwest of Manhattan). He's a former big game guide and can tell the difference between a mountain lion and big Labrador Retriever, so I trust him. There are loads of deer even in the suburbs of New Jersey.