I have mated many thyla. here are some pointers. Breed in numbers. Watch videos and build three walls high and a ceiling. Than you jump up and hop off and they will spin around. put male in middle and 2 females on each side. Afterwards take females off wondering, move them and start next batch. You will end up with a lot of thyla, but you can pick and choose until you get the right ones.
Thylacoleo are capable of pinning down flyers in mid-flight (anything but the Quetz and Wyvern, I believe), other Thylacoleo, and even Therizinos. You can also jump from object to object by holding down the jump button while pouncing from a tree or cliff (have to hit it at the right angle, however). Upvote to inform others!