Deinonychus nests are found throughout the White Cliffs in the bottom right of the map, and are often accompanied by multiple wild deinonychus who will attack as soon as you take an egg.
For a larger map including the markers, see the Explorer Map.
It is advised to use a flyer if you're looking to steal the eggs. You could either wait for them to get distracted when they notice a wild dino nearby or kill them when you're standing on a rock that is just out of their attack range.
Console command to get list of all Deinonychus Nests on map: cheat getallstate DeinonychusNest_C
Console command to spawn Deinonychus Nest: cheat summon DeinonychusNest_C
Be careful! Character will get stuck in it! To get out use console command: cheat ghost | cheat fly
Nest will disappear after some time.
Console command to destroy all Deinonychus Nests on map: cheat destroyall DeinonychusNest_C