The description of Stunning Fist says that the unarmed strike must do damage to the target before they need to make a save against the stunning effect. Does that include nonlethal damage? Can a Monk choose to deal nonlethal and still apply Stunning Fist?
I don't see why not.
Non-lethal damage is still damage.
I must breathe air to remain alive. Sometimes I breathe fresh air. Sometimes I breathe polluted air. Regardless, it's all air and it meets the requirement for keeping me alive.