Couple of Hints:
First, Triceratops Encounter is no longer a "timed" experience. In other words, once you enter a Triceratops paddock, you and your party are welcome to stay as long as you like - the program is continuous. So if your child is not picked to pet the Triceratops, you are welcome to stick around until the next opportunity (about every 10 to 15 minutes).
Second, there is a height requirement to pet the Triceratops. I would recommend asking the greeter at the front of the attraction if your child is tall enough prior to entering the queue. I am not sure of the specific height needed (probably around 38 to 40 inches). The requirement is for the need for the child to reach over the paddock fence ON THEIR OWN to pet the Triceratops. For safety reasons, due to the incredible (and sometimes unexpected) movements of our Triceratops) parents may not hold their children up to pet the Triceratops.
Finally, you will want your children to be near the head of the Triceratops, right up along the fence - in order to be picked.
Hope this helps