The phrase good cop, bad cop is used to refer:
– to a police interrogation technique in which one officer adopts a threatening approach while the other feigns a sympathetic or protective attitude;
– and, by extension, to a method designed to wear down an opponent by alternating a harsh, unrelenting approach with a kind, compassionate attitude.

This interrogation technique, also called Mutt and Jeff, friend and foe and joint questioning, was described in Human Resource Exploitation Training Manual (1983), by the Central Intelligence Agency (CIA), a federal agency in the USA responsible for coordinating government intelligence activities:

JOINT “QUESTIONERS” (AKA FRIEND AND FOE)

The commonest of the joint “questioners” techniques is the “friend and foe” routine. The two “questioners” display opposing personalities and attitudes toward the subject. For example the first “questioner” displays an unsympathetic attitude toward the subject. He may be brutal, angry, or domineering. He makes it plain that he considers the subject the vilest person on earth. His goal is to alienate the subject, at the height of the alienation. The second “questioner” takes over, sending the first out of the room. The second “questioner” then displays a sympathetic attitude toward the subject, perhaps offering him coffee and a cigarette. He explains that the actions of the first “questioner” were largely the result of his lack of knowledge in dealing with people and lack of human sensitivity. If brutes like that would keep quiet and give a man a fair chance to tell his side of the story, etc., etc.
The subject is normally inclined to have a feeling of gratitude towards the second “questioner”, who continues to display a sympathetic attitude in an effort to enhance the rapport for the “questioning” which will follow. If the subject’s cooperativeness begins to fade, the second “questioner” can state that he cannot afford to waste time on sources who fail to cooperate and imply that the first “questioner” might return to continue the “questioning”.
When this technique is employed against the proper source, it will normally gain the source’s complete cooperation. It works best with women, teenagers, and timid men.

The earliest instance of the phrase good cop, bad cop that I have found is from a letter by one Donn Crockett, published in The Fresno Bee (Fresno, California, USA) of Tuesday 23^rd December 1969:

Editor of The Bee — Sir: The current campus rumpus at Fresno State College is not unique and was probably inevitable, but it disturbs an old alumnus of the ivy-covered old-campus days.
Now, under the guidance of Gov. Ronald Reagan ¹, the FSC administration has become chillingly like that in Washington. The other night, on KMJ-TV, the writer watched Dr. Falk ² carefully read a prepared statement, followed by Dr. Fikes ² and his ad lib diatribe aimed at the sociology and psychology departments. President Nixon ³ and Mr. Agnew ⁴ could have done no better. The technique was reminiscent of the “good cop-bad cop” method of impressing suspects.

¹ Ronald Wilson Reagan (1911-2004) was the 33^rd Governor of California from 1967 to 1975, and the 40^th President of the United States from 1981 to 1989.
² Against a background of political unrest at Fresno State College, Karl Falk was appointed as acting president on 28^th October 1969; he appointed James Fikes as executive vice president five days later.
³ Richard Milhous Nixon (1913-94) was the 37^th President of the United States from 1969 until his resignation in 1974.
⁴ Spiro Theodore Agnew (1918-96) was the 39^th Vice President of the United States from 1969 until his resignation in 1973.

The second-earliest occurrence of good cop, bad cop that I have found is from Body-beautiful Fred loses his cool: Peter Wilson gets a rub-down at a health spa, published in The Sun (Vancouver, British Columbia, Canada) of Saturday 12^th February 1972—the author has just joined a health spa, and an instructor, Fred, has prescribed him “a simple set of exercises that will not tax” him:

First it was the bicycles for a couple of minutes at an alleged 35 miles an hour, then the vibrator belt front and back followed by a surfboard-like machine that had me hanging on and doing a kind of hula.
These snaps to the spine were followed by situps administered in a variation of the good cop, bad cop routine for breaking down suspects. Fred told me to do 15 situps and then relax. Meanwhile he called another instructor over while he went to answer a phone call. The other instructor immediately upped the situp quotient to 25 and smiled as I turned blue, purple and finally a bright orange.

In the Chicago Tribune (Chicago, Illinois, USA) of Sunday 4^th August 1974, Jon Margolis used the phrase when reporting on the Judiciary Committee of the House of Representatives, which, the previous Tuesday, had voted three articles of impeachment against President Richard Nixon (Charles William Sandman Jr. (1921-85) was a Republican Representative from New Jersey, and Charles Edward Wiggins (1927-2000) was a Republican Representative from California):

Nixon’s most outspoken defenders, Sandman and Wiggins, were like a good cop-bad cop act. Sandman was sarcastic and bombastic. “Isn’t it amazing?” he would ask over and over, pointing out what he thought were discrepancies in the evidence.
Waving a magazine, perching his glasses on the end of his nose, wading in like the boxer he once was, he tried to bludgeon the case against Nixon.
“Now,” he said, “if I went thru this thing paragraph by paragraph I could cite with great detail no Presidential involvement. They know it, you know it, and I know it.”
Wiggins was soft-spoken and courteous and technical. He tried to carve into the evidence, exposing inconsistencies. Debating the article citing Nixon for withholding evidence, he said that the majority had already passed two articles of impeachment based on what it called a “surfeit” of evidence. “Now,” he said, “we seek to impeach him because he didn’t give us the evidence to do the job.”