"Cowboy diplomacy" was a term which was used by Captain Jean-Luc Picard and Ambassador Spock as a form of insult, and refers to a diplomatic effort being made that involves means that are outside normal and acceptable practice. It was named for the cowboy of American history and fiction.
After meeting Spock on Romulus in 2368, Picard told Spock that the kind of cowboy diplomacy he had engaged in throughout his long history of service to the United Federation of Planets would not so easily be tolerated anymore. Spock responded that he had participated in cowboy diplomacy long before Picard had been born. (TNG novelization: Unification)
When the Romulan underground arranged for the Vice-Proconsul M'Ret and his two top aides to defect to the Federation, and Stefan DeSeve—who had earlier defected to the Romulans, but grown disillusioned with Romulan life—decided to return to the Federation, Spock had him relay a message to Picard, telling him that it involved more cowboy diplomacy. (TNG episode: "Face of the Enemy")