After a first pregnancy ended in miscarriage, the couple’s daughter, Liliana, was born in 2002, and for nearly two years Ms. Goldberg raised her on her own, though Mr. Lines came by two or three times a week to pitch in with changing diapers, feeding and playing with their daughter. Eventually Ms. Goldberg and Mr. Lines decided to move in together; had a son, Tulliver; bought a Victorian house, and, finally, married — in a columned, open-air rotunda in a park near their home, with Ms. Goldberg wearing a maroon velour dress purchased at a thrift store and both children in attendance.

Image FIRST OWNER Carey Goldberg with her husband, Sprax Lines, and children, Liliana, 8, and Tulliver, 5. Credit... Jodi Hilton for The New York Times

It was after Ms. Jones, too, was settled into love and motherhood — now 46, she and her husband, Phil Jones, a forensic auditor, live in a shingled early 1900s house not far from Ms. Goldberg’s with their 5-year-old son, Gareth — that the book idea came up. The writers didn’t seriously discuss it, however, until Ms. Ferdinand was well on her way to a healthy pregnancy. “Beth and I had our kids, and we were waiting for Pam to have her happy ending,” Ms. Goldberg said.

Ms. Ferdinand, now 44, a former reporter for The Washington Post and The Boston Globe, lives in the Chicago area with her fiancé, Mark Thomas, a photographer and information technology professional, and their 2 1/2-year-old daughter, Emma. But much of the writing of the book took place while she was still living in Boston. The authors first worked on their individual stories independently. Then together they chopped up their accounts into alternating chapters, with Ms. Goldberg, who set in motion the chain of events with her purchase of the donor sperm, kicking things off in Chapter 1.

After the first literary agent the writers approached with the manuscript they were calling “The Lucky Sperm” turned them down, they contacted another agent, Denise Shannon. “When I first heard about it, what popped into my head was the sisterhood of the traveling sperm,” Ms. Shannon said in a phone interview. After the authors streamlined their manuscript and came up with a title that didn’t have the word “sperm” in it, Ms. Shannon submitted “Inconceivable Happiness” to publishers, and within a week she had a pre-emptive deal with Little, Brown & Company “in the mid six figures,” according to the writers. Little, Brown renamed the book yet again and released it last month, with an announced initial print run of 30,000 copies.

“It isn’t just a fairy tale,” said Judy Clain, executive editor at Little, Brown. The company would not release sales figures, but Ms. Clain acknowledged in a phone interview that the book “wasn’t flying off the shelves” — even after the three women appeared on the “Today” show to promote “Three Wishes.” At one point last week it was ranked No. 27,519 on the Amazon best-seller list.

IN the early chapters, the authors recount their experiences as single women, which involved nice-but-no-spark relationships as well as creepy blind dates arranged through matchmaking sites. At one point Ms. Jones paid a matchmaker named Zelda $2,000 to find her a man — and then demanded a refund. “One guy was a right-wing banker who rarely stepped foot outside his office except to drive his Miata around Wellesley,” she writes, “the other a divorced back surgeon who was so tired on our three dates that I had to resist snapping my fingers in his face.”