Only ways I know to get falcon troops are:
1. Hold a castle that is falcon culture orginally, get the ridere fealcons.
2. The Aepele falcons will be seen running around as peasant rebels in the area. Blunt weapon them take them as prisoners and recruit them, these scale up to reweards.
There are a few other sneaky ways to get them but these work the best in my experience, even if you are a vassal you don't get any so don't waste your time.