Can a priest order us to stand when receiving Communion?
Our priest does not want to give us Communion on the tongue while we are kneeling. He argues it is too hard for the priest to lean down like that. Does he have the authority to order us to stand for Communion?
No, your pastor does not have any authority to place such a restriction. Your right to receive Communion on the tongue while kneeling is guaranteed by Church law, and a local pastor cannot change this. He is within his rights to ask that you stand, so that he doesn't have to change his posture while distributing Communion, but you are within your rights to decline this request if you feel more comfortable or reverent doing it the other way.
The argument that it is too hard for the priest to give Communion to people who are kneeling is specious. Catholic priests were doing that for centuries, and in the old days it required them to stoop even more since the communicants were kneeling while the priest stood on the platform in front of them, meaning their heads were often even lower with respect to him.
If it is your priest's habit to position himself on a the bottom step in the sanctuary when distributing Communion (perhaps he is shorter than most communicants), he easily can take a step down to give Communion to the kneeling, then can take one step up to give Communion to someone who is standing.