The simplest and (almost) safest way to tame a thylacoleo:

1. You will need the best crossbow you can get, some tranq arrows, and be wearing flak armor. Also, very important, a harpoon launcher loaded with net projectiles;

2. Then, wield your harpoon, mount your flyer, and go around flying low in the redwoods showing off the thyla bait (that would be you, btw);

3. When you inevitably get jumped on and are in the middle of a fanged hug on the ground, just shoot your net at the thyla, then pepper it with tranqs on the head before it gets free to murder you;

4. Afterwards, just guard your thyla until tamed and pray no nasties come out: a cryopoded Rex does wonders for emergencies. Good luck!