Only obtained by searching for eggs, just like wyverns and drakes. Watch out for the pack though. They protect the nest and with their latching and bleeding abilities, they can be quite formidable. Either be quick about sneaking in and grabbing eggs, or kill them all. There is no in between...
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.
Deinonychus eggs can only be gotten like the rock Drake or wyverns, you just steal a fertilized egg from their nest. Normally I would use a snow owl to freeze it while my tribe mate grabs the eggs. Or you can have a gun and a dinosaur with good melee. (The gun to shoot it if it latches on your mount). And kill them and grab the eggs.
For all I know they are only found in the white cliffs in packs. There is a set of ruins with bridges. The nests that I know of are near the bridges guarded by rock elementals as well as the new fluffy raptor