Imperious
Without the sun of my life
Nice. Maybe when we can spare the time from the Lightfangs we can go on a trip to the world's edge mountains to try to do the same. We'll make a trip of it! A familiar could help a lot in finding such more quickly and Ghur would help a lot with the actual taming.Quite often two Asur who happen to ride male and female griffons agree to let their mounts meet and produce baby griffons.
Aside from that, most of the time a prospective rider will venture into the wilderness to look for a juvenile griffon, old enough to have been kicked out of their parents' nest but still not fully grown.
Not because they think going for the nest is immoral or something, but because having someone else do it for you or help you with is considered terribly gauche, and having to fight or sneak past one or quite possibly two adult griffons on your own is not something most elves want to take a crack at.
If it's plausible to both find and tame a juvenile rather then an egg then we could also try to find one that's familiar worthy.
Going to be funny to have a Griffin refer to the bird as big brother if they happen to be of a similar enough species.