The couple claims a social worker helped their 15-year-old son "tremendously" reduce his homosexual urges, but the law now prevents them from taking him to a "gay conversion" therapist in the state.
While supporters of the therapy have encouraged those who are interested to seek the conversion therapy from unlicensed counselors, the family claims they tried it, but it was ineffective.
The unlicensed counselor the couple went to "did not seem to share the same scholarly view of the issues surrounding sexual orientation change efforts counseling as the many experts in the field," according to the complaint.
The couple is arguing the teen needs the therapy because he "frequently thought of killing himself because he did not like himself ... He remembers having a bias against the male gender and thinking boys were stupid because his mother talked negatively about his father."
"He experienced feelings of despair because he believed that he would never be good enough if he remained a boy," the complaint adds.
New Jersey is the second state to ban the controversial conversion therapy. A similar law was banned in California in August by the Ninth Circuit Court of Appeals.
Supporters of the ban cite the American Psychological Association and other professional groups who say there's no proof the therapy is effective.
"Research indicates that family interventions that reduce rejection and increase acceptance of their child and adolescent are helpful," read the association's report on sexual orientation change efforts.
Christie is likely to be re-elected as New Jersey's governor on Tuesday.