Why is nobody talking about tapejaras? You can latch onto a solid surface and shoot down at it and tranq it. Works especially well in the redwood forest. Just look out for thylacoleos waiting to ambush you.
If you use the bear trap strategy which is if you lead it into a Dino gateway that is shaped in a triangle and with a bear trap in the middle (Large Beartrap) and when it is stuck you must put a dinogate behind it to trap it and then knock out. (hope this helped and "If" I win could it be an Xbox voucher, thanks.)
If you bring your high health Spino, hit the Rex once and it will just get distracted attacking your Spino instead of you. Just dismount and tranq it then when its running away just chase it as you tranq it then it shall get unconscious. My plan became successful. The rex i tamed was a.lvl 10.