There's not just a problem with capturing the wyverns, but also being able to "break" (AKA domesticate) them.
For example, if you capture an adult wild horse, it is incredibly hard (some say it's just impossible) to break them. You need to have a horse from a young age--not necessarily birth, but pretty young, so they bond to you. Normally they start training them at 18-24 months.
For wyverns, trying to take a youngling from its mother would be dangerous. Therefore probably the easiest way to do this would be to steal eggs while the mother is away.
Note, that's just how you would get the first few. After a while, when you have a population of domesticated wyverns, it would be much easier to work with wyvern mothers that are domesticated themselves.
In this society, they would probably highly prize the people who have a good animal instinct for bonding with the wyverns.
Note that not all animals are tame-able. For example the zebra, contrary to appearing to be very similar to a horse, is not as related as you might think. People have tried taming zebras many times and failed. So with that rationale, you do have the option of claiming that your wyverns are the same way; their disposition isn't right for taming. Most predators are difficult to tame.