If you are alone, ride a pteranodon. This is because they cannot latch onto a pteranodon, but they can latch onto an argentavis. Lead the deinonychuses away from the nest and into a group of brontosauruses. Agro the brontos and make them hit the deinonychuses, and then watch carnage ensue. Rinse and repeat until the deinonychuses have all died, make sure brontos aren't agroed and then safely snatch the eggs from the nests. Using a whip is an optional choice to make things run smoother and faster. After this process, go somewhere else for a few minutes and come back to do it again. With very little practice, this can be a very effective method.
If there are no brontos in the area, use the pteranodon as a weapon. Swoop in and twirl into the deinonychuses until they die. WATCH OUT for raptors. They WILL dismount you in a heartbeat, whether they were targetting you beforehand or not. After the deinonychuses are dead, swoop in and snatch the eggs before leaving and repeating the process.
You can't tame these guys by knocking them out. Instead, you need to steal their fertilised eggs (just like wyverns and rock drakes), hatch them and raise them, just a bit harder than knocking them out. The eggs can, of course, be found in their nests and do be careful while trying to steal one as the Deinonychus is very territorial. Hope this helps :)
Here's how to steal one early game: If you spawn in at chalk hills 3 and spawn next to a pond walk opposite to the pond. There are some nests right there. Snatch one quickly and run off the cliff next to the pond. Be careful and make sure to fall into the water. From there make a left and you should get to a beach area. From there it should be easy to find your base.
1. Tame a kangaroos 2. Have a tribe mate with a whip in the pouch 3. Quickly jump on a nest and have your tribe mate whip the egg into his inventory 4. Jump away! No one has to dismount so there’s basically no risk