There are natural wyvern traps all around the map. They look like a series of triangles. There are two on the beach almost directly across from each other around 65 x 23. Aggro the wyvern and lead it into the trap. A tamed wyvern with rider will fit under the bottom edge of the trap letting you go through and trapping the wild wyvern. It can then be tranquilized and you can pull tve crystal off. They rarely are able to get out of these traps so easy to kill them after.
I don’t know if I’m stupid and it tells you this but I struggled with this for a bit and figured out that the wyverns of the same type Cant hurt each other which is something I figured out while shooting my blood wyverns blood at a blood wyvern for 15 minutes and it did nothing 😅