The American Psychiatric Association and the World Health Organization, among other mental health groups, have cited the potential risks of reparation therapy, including "depression, anxiety [and] self-destructive behavior," according to the lawsuit.
Chaim Levin, the most vocal of the plaintiffs, is now 23 and a gay rights advocate who writes a blog, Gotta Give 'Em Hope.
He grew up in a Jewish ultra orthodox community in Brooklyn where religious leaders threw him out of the Hebrew-speaking yeshiva at the age of 17, when they learned he was gay.
Levin told ABCNews.com that he had been abused as a boy and that he was "confused" by his sexuality and took a rabbi's advice and began 18 months of gay conversion therapy at JONAH.
[Levin filed a civil lawsuit against his cousin in July, alleging he was abused for three years from the time he was 6.]
When Levin met co-director Goldberg, he said the defendant told him JONAH could change his sexual orientation, "as long as I tried hard enough and put enough effort into it."
"He told me, 'You will marry a woman and have a straight life,'" said Levin.
"Given where I came from, with three older siblings who were married with kids and not knowing any gay people or English, I was sure I could change," he said. "That was the theology."
Levin first did a retreat with Downing, then saw him weekly at therapy sessions in Jersey City.
"A lot of the therapy involves reliving the experience," he said. Levin alleges he was forced to relive the sexual abuse by his cousin, "with no counseling afterwards."
But the most "humiliating" experience, the one that Levin alleges made him quit therapy, was being asked by Downing to take off his clothes, article by article and told to touch his "private parts" -- to hold his penis in front of a mirror to "be in touch with my masculinity."
"I told him I wasn't comfortable, but I desperately wanted to change and was ready to do anything," said Levin. Afterward, he said he felt "degraded and violated."
Today, Levin no longer identifies as orthodox, but said his parents have been "supportive" of the lawsuit.
Some Jewish denominations and many congregations are inclusive of homosexual congregants, and even New York's orthodox communities are more open-minded now, according to Levin.
"I had gone for help and they had misrepresented themselves," he said.