“Don’t agonize, organize” was a 1970s slogan of the women’s movement, specifically the older women’s movement for civil rights. Both Florynce Kennedy (1916-2000) and Tish Sommers (1914-1985) popularized the slogan, and one of them probably coined it.
 
“Don’t Agonize—Organize” was cited in a December 1971 advertisement about Christmas shopping. A March 1973 profile of Florynce Kennedy by Ms. Magazine credited her with “Don’t agonize. Organize.” Tish Sommers, then chair of the National Organization for Women’s Task Force on the Older Woman, used “don’t agonize, organize” in October 1974.
   
 
Wikipedia: Florynce Kennedy
Florynce Rae “Flo” Kennedy (February 11, 1916 – December 22, 2000), was an American lawyer, activist, civil rights advocate, and feminist.
 
Wikipedia: Tish Sommers
Letitia “Tish” Sommers (Cambria, California, 1914-1985) was an American author, a women’s rights activist, and the co-founder and first President of the Older Women’s League.
 
Google News Archive
13 December 1971, Bangor (ME) Daily News, pg. 6, col. 8:
Don’t Agonize—Organize.
Christmas Shop
A Little At A Time—
Or All At Once.
(The Back Porch—ed.)
   
Ms. Magazine (March 1973)
WEB EXCLUSIVE | SUMMER 2011
The Verbal Karate of Florynce R. Kennedy, Esq.
By GLORIA STEINEM
Watching the new HBO documentary Gloria: In Her Own Words left us nostalgic for the early days of Ms. and eager to hear about even more of the women who launched the contemporary feminist movement–especially the memorable Flo Kennedy. Just a few moments of footage of Kennedy (who died in 2000 at age 84) at the 1972 Democratic National Convention made it abundantly clear that she was a force to be reckoned with. So we went to the Ms. archives and unearthed a feature from the March 1973 issue in which Gloria Steinem pays homage to the “infinitely quotable Flo.” Here is the original piece:
(...) 
“Don’t agonize. Organize”
 
25 October 1974, Seattle (WA)

, “Older women urged to fight for rights” by Sally Gene Mahoney, pg. C1, col. 4:
“In order to make changes,” she continued, “we’re going to have to ‘rattle the cages.’ I say, ‘Don’t agonize, organize.’ We must form alliances and coalitions to force social change…until we organize and move in our self interest, we’ll continue as a powerless group.”
(Tish Sommers, chair of the National Organization for Women’s Task Force on the Older Woman—ed.)
 
25 July 1975, Register-Republic (Rockford, IL), pg. A13, col. 1:
Organize, don’t agonize,
say middle-age women
By LYNNE ABRAHAM
(...)
“Don’t agonize—organize,” feminist leader Florence Kennedy says. And that’s what many mature women are doing. OWL—the Older Women’s Liberation—is pressing for an end to age and sex discrimination. The newest feminist group is the National Women’s Agenda, an umbrella organization of 75 women’s groups representing more than 30 million women.
 
OCLC WorldCat record
Don’t agonize organize
Author: Otto Sam Folin
Publisher: New York, N.Y. Program Agency of The United Presbyterian Church U.S.A. and the Division of Corporate and Social Mission of the Presbyterian Church U.S. 1975.
Series: Church and society, v.65, no.6. 
Edition/Format: Book : English
 
Google Books
Perspectives on Aging:
Exploding the Myths:
A lecture series funded by the Colonial Penn Insurance Group
By Priscilla W. Johnston, Contributing Editor
Cambridge, MA: Ballinger Pub. Co.
1981
Pg. 83:
I think it was a woman who coined the slogan, “Don’t agonize, organize.”
 
Google News Archive
18 February 1983, Durant (OK) Daily Democrat, “Older Women’s League FIghts Discrimination” by Patricia McCormack (UPI Health Editor), pg. 3, col. 1:
Women in a movement led by Californian Tish Sommers refer to themselves as “coming of age” and use such slogans as “age is becoming,” “don’t agonize, organize.”
 
She heads OWL—Older Women’s League—an advocacy group that now counts 50 chapters nationwide and more than 5,000 members, most of whom are women 45 to 70 years of age.
 
OCLC WorldCat record
Don’t agonize, organize! : your life is your business
Author: Regina Muster
Publisher: Eagleville, PA : DNA Press, ©2006.
Series: Nuts & bolts series. 
Edition/Format: Book : English
 
OCLC WorldCat record
Don’t agonize, organize your office now! : simple solutions for your office organizing challenges
Author: Diane A Hatcher
Publisher: North Charleston, S.C. : BookSurge, ©2007.
Edition/Format: Book : English
 
The Raw Story
Pelosi: ‘Our success as a nation really depends on our success of women’
By Kay Steiger
Thursday, July 18, 2013 15:12 EDT
In a meeting with reporters on Capitol Hill, House Minority Leader Nancy Pelosi and Rep. Rosa DeLauro (D-CT) rolled out on Thursday what they called a campaign to economic issues important to women.
(...)
Pelosi added that “My key phrase was always, don’t agonize, organize. We have a problem with equal pay, we have a problem about child care, we have a problem about not being able to take sick leave. Let’s organize around this. And believe me when I tell you this: We would rather they join us in this rather than having to use it as a political weapon.”