"Coffee, tea or milk?” was the familiar question that an airline stewardess (now called “flight attendant") offered passengers in the 1950s and 1960s. The book Coffee, Tea or Me? (1967) by Trudy Baker and Rachel Jones (with Donald Bain) about the lives of young stewardesses made popular the now-dated twist on the phrase.
There are a “coffee, tea or me” citations in October 1962 and in the October 1965 True magazine (a men’s magazine, similar to Esquire), so it appears that the book’s title did not coin the phrase.
Wikipedia: Coffee, Tea or Me?
Coffee, Tea or Me? is a book of memoirs by Trudy Baker and Rachel Jones written with Donald Bain and first published in 1967. The book depicts the anecdotal lives of two lusty young stewardesses. Capitalizing on the success of the publication, Donald Bain wrote three sequels: The Coffee Tea or Me Girls’ Round-the-World Diary (1969), The Coffee Tea or Me Girls Lay It on the Line (1972) and The Coffee Tea or Me Girls Get Away from It All (1974). A TV film of the same title, loosely based on Coffee, Tea or Me? was made in 1973.
14 October 1962, The Register (Danville, VA), “European Airline Initials Intrigue Overseas Tourists” by Erskine Johnson (NEA), pg. 8-D, col. 2:
He was a veteran airline passenger, with a million mile card to prove it. He was also a wolf with a special yen for stewardesses. To win a bet, one of them finally thought of a gag based on habit. She came down the aisle asking, “Coffee, tea or milk?” of all the passengers except our friend.
To him she said, “Coffee, tea or ME?”
His answer was loud and clear. “Tea,” he smiled, missing the best offer he ever had.
October 1965, True, humor page, pg. 140, col. 2:
My friend Bev, a former airline stewardess grounded by marriage, finally went back to work as a stewardess for a large company on their executive airplane.
Thrilled by the prospect of flying again, she reported to the pilot on board the aircraft for her first trip. Attempting to be funny as well as friendly, she quipped, “Hi! What’ll it be—coffee, tea or me?”
With a quick appraising glance the veteran pilot replied, “Suit yourself, sister. Whatever’s the easiest to make.”
R. J. Putman
OCLC WorldCat record
Coffee, tea, or me?; The uninhibited memoirs of two airline stewardesses,
by Trudy Baker; Rachel Jones
Type: Book; English
Publisher: [New York] Bartholomew House 
Internet Movie Database
Coffee, Tea or Me? (1973) (TV)
Plot:An airline stewardess juggles a life that includes a husband in Los Angeles and another one in London.