The cosmetics founder Mary Kay Ash (1918-2001) is often credited with: “If you think you can, you can. If you think you can, you’re right.” However, she admitted that she received the inspiration from Norman Vincent Peale and his book, The Power of Positive Thinking.
 
The phrase isn’t original with Norman Vincent Peale, either. It was used frequently in sports thorughout the 1900s.
   
   
Wikipedia: Norman Vincent Peale
Dr. Norman Vincent Peale (May 31, 1898 – December 24, 1993) was a Protestant preacher and author (most notably of The Power of Positive Thinking) and a progenitor of the theory of “positive thinking”.
(...)
Teachings
“Positive thinking,” as described by Peale could be broken down into a three step process of practicing repeated self-hypnosis, attaining “divine” or God’s power to use for oneself, and eliminating and avoiding all negativity in life.   
 
Wikipedia: Mary Kay Ash
Mary Kay Ash (May 12, 1918–November 22, 2001) was a U.S. businesswoman and the founder of Mary Kay Cosmetics, Inc.. Born Mary Kathlyn Wagner in Hot Wells, Texas, Ash worked for several direct sales companies from the 1930s until the early 1960s, achieving considerable success as a salesperson and trainer. Frustrated, however, at being passed over for promotions in favor of men, she retired in 1963, intending to write a book to assist women in business. The book turned into a business plan for her ideal company, and in September 1963, Ash and her son, Richard Rogers, began Mary Kay Cosmetics with a $5,000 investment. The company originally operated from a storefront in Dallas but grew rapidly, particularly after Ash was interviewed for CBS’s 60 Minutes in 1979. The famous pink Cadillacs awarded to top sales people were the most visible sign of the company’s success.
 
Ash was widely respected, if not always understood, for her unconventional approach to business. She considered the Golden Rule the founding principle of Mary Kay Cosmetics, and the company’s marketing plan was designed to allow women to advance by helping others to succeed. Unfailingly supportive and enthusiastic, she advocated “praising people to success,” and her slogan “God first, family second, career third” expressed her insistence that the women in her company keep their lives in balance.

Both during her life and posthumously, Ash received numerous honors from business groups, including the Horatio Alger Award. A long-time fundraiser for charities, she founded the Mary Kay Ash Charitable Foundation to raise money to combat domestic violence and cancers affecting women. Ash served as Mary Kay Cosmetics’ Chairman until 1987, when she was named Chairman Emeritus. She remained active in the company until suffering a stroke in 1996. Richard Rogers was named CEO of Mary Kay Inc. in 2001. At the time of Ash’s death, Mary Kay Cosmetics had over 800,000 representatives in 37 countries, with total annual sales over $2 billion at retail.
 
Mary Kay authored three books, all of which became best-sellers. Her autobiography, Mary Kay, has sold more than one million copies and appears in several languages. Her business philosophy, Mary Kay on People Management, continues to be a great source of wisdom and has been included in business courses at the renowned Harvard Business School. Mary Kay Ash’s third book, You Can Have It All, was launched in August 1995 and, remarkably, achieved “best-seller” status within days of its introduction. Her speeches and quotes continue to inspire the women of the Mary Kay sales force. Mary Kay suffered a stroke 5 years before she died. She died November 22, 2001. 
 
Google Books 
The Forest
by Stewart Edward White
New York, NY: The Outlook Company
1903    
Pg. 175:
“That’s right,” said Del, imperturbably. “If you think you can, you can.”
   
22 June 1914, Lincoln (NE) Daily News, pg.  5A, col. 1:   
“It’s the old con-feed-ence that wins,” aid Del Howard, now manager of the San Francisco Seals. “That’s all there is to baseball. If you think you can, you can. If you think you can’t, you can’t. If you keep thinking you can win, the teams ahead of you will soon begin to believe it, and come back to you.”
   
8 October 1921, Chillicothe (MO) Daily Constitution, pg. 2, col. 3:
The State High School Inspector, Mr. Cole visited Dawn High school Tuesday of last week. He was well pleased with the work and equipment, especially the library. He gave a very interesting talk. The theme of his talk was “If you think you can, you can.”
   
12 July 1923, Frederick (MD) News, pg. 4, col. 1:
“If you think you can, you can.” 
 
28 May 1937, Wisconsin Rapids (WI) Daily Tribune, pg. 6, col. 4:
“Our deepest desires are God’s promises,” she told me, earnestly. “We can do a thing if we stick to it. If you think you can, you can.”
   
22 November 1940, Nebraska State Journal (Lincoln, NE), pg. 9, col. 5:
AMES, Ia. (AP). As the day for the annual Iowa State-Nebraska gridiron classic draws near, everything appears to be normal on the surface, but there is an undercurrent of the most intense desire on the Iowa State campus to whip the Huskers.
 
The chalked sign on the team’s locker room blackboard which says, “If you think you can, you can; if you think you can’t, you’re right,” reflects something of the entire school’s attitude toward Nebraska.
 
14 November 1945, Fitchburg (MA) Sentinel, “All Sorts” by Barbara Allen, pg. 4, col. 2:
In simple language this means: If you think you can, you can; if you think you can’t, you can’t.
 
9 October 1954, Holland (MI) Evening Sentinel, pg. 4, col. 2:
Years ago when Tom Shevlin went to Yale as director of athletic activities he found a football team which was consistently losing games, but he converted it into a winning team. He accomplished this feat by changing the standards by which they were measuring themselves. Said Shevlin to his athletes: “If you think you can, you can! But if you think you can’t, then the football field is no place for you!”
 
3 October 1964, Pasadena (CA) Independent, pg. 5, col. 1:
You Can If You Think You Can
By Norman Vincent Peale
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I had a problem one time about raising money for the church and I went to consult Brother Andrews about it. I told him I didn’t think I could raise that amount of money. He said, “If you think you can’t, you can’t; but if you think you can, you can. So, start thinking positively.”
   
24 July 1965, Fremont (CA) Argus, pg. 3, col. 5:
“Charley Paddock was a great speaker. He loved to talk with young people and he had one great theme: ‘If you think you can, you can. If you believe a thing enough, it can come to pass in your life.’”
 
Google Books
The Positive Principle Today
by Norman Vincent Peale
EnglewoodCliffs: Prentice-Hall
1976
Pg. ?
YOU CAN IF YOU THINK YOU CAN
 
Google Books
Seeds of Greatness:
The Ten Best-Kept Secrets of Total Success
by Denis Waitley
New York: Pocket Books
1984
Pg. 227:
You can upset mcenroe or Austin, win the marathon in Boston. If you think you
can, you can. 
     
20 October 1985, New York Times, “Reading Their Way to the Top—Books That Made a Difference,” book review, pg. BR45:
Mary Kay Ash
Chairman of Mary Kay Cosmetics.
 
“The Power of Positive Thinking” by Norman Vincent Peale is still a classic. Especially in business, if you think you can, you can. And if you think you can’t, you’re right.
   
Google Books
Simpson’s Contemporary Quotations
by James Beasley Simpson
Bostn, MA: Houghton Mifflin
1988
Pg. 93:
MARY KAY ASH, Chairman, Mary Kay Cosmetics Inc.
“If you think you can. you can. And if you think you can’t, you’re right.”