What is the ruling on agreeing with friends to abandon a specific sin, making a covenant to that effect, then punishing whoever violates the covenant with reprimand or beating, then abandoning the condition of punishment while continuing to adhere to the covenant?

One must avoid all sins. It is not permissible for a sinner to disclose his sins about himself, because it is obligatory for a Muslim to conceal his own sins if he commits one. Disciplining a transgressor by beating or scolding is within the authority of the ruler or the judge. If this agreement leads to refraining from a specific sin, then it is a good thing. Breaking it does not entail expiation because there is no wording that indicates a commitment. Expiation is only obligatory for someone who makes a covenant with Allah Almighty regarding something and then breaks the covenant.