The lawyers for the estranged couple were drafting an agreement shortly before 6 p.m., and Superior Court Judge Karen Cassidy was standing by for its completion, Thaler-Gerber said.
Should custody be settled, the McGreeveys and their lawyers would return Monday and begin settlement talks on alimony and child support, she said.
Should those succeed, the remaining issue would be Dina Matos McGreevey's claim of marriage fraud.
Thursday's testimony was given behind closed doors because it dealt with custody of the couple's 6-year-old daughter. There was no immediate word on who or how many people had testified.
The former governor and his wife split in 2004 after he resigned in disgrace over a gay affair. They had been married for four years.
James McGreevey stepped down during his first term in office after a nationally televised speech in which he acknowledged being "a gay American" and said he had an affair with a male staffer.
The staffer has denied the affair and claims he was sexually harassed by McGreevey.
In the 3½ years since the breakup, James McGreevey took up residence at the home of his boyfriend and began studying for the Episcopal priesthood while Matos McGreevey became a sometime analyst on cable television shows. Both wrote tell-all books and promoted them on Oprah Winfrey's television show.
