It may be possible to fly passenger pigeons using specialized drones — but a more natural solution may be achievable using homing pigeons as surrogate flocks to lead the passenger pigeons from one site to another.
In thinking of pigeons, there have been many pigeons born and raised in captivity that were fostered by surrogate parents (such as Victorian crested pigeon chicks raised by nicobar pigeons and nicobar pigeon chicks raised by rock pigeons).