Darryl Fletcher and Brandon Ventimeglia, both 26, will be able to see two-year-old Darryl Scott every Wednesday and on alternate weekends while the row continues over whether they have parental rights.
While pregnant, the boy's mother, India Scott, 25, had told each man that he was the father of Darryl and, after he was born, they both helped to care for him.
Neither knew about the other's involvement until they both filed for custody in April after discovering that Ms Scott planned to move to Virginia with her new husband.
She has still not said who she thinks is the biological father.
Under Michigan law, an equitable parent is recognised by the public, the court and the child as the parent. No genetic link is required.
Mr Fletcher's lawyer, Karen Russell, said: "The law has not been able to keep up with family changes and moves. The equitable parenting doctrine is an inventive way to recognise a bond has taken place without a blood connection."
Ms Scott's lawyer, Barry Fayne, vowed to fight the custody request.
"How many people from outside of the gene pool [of the family] should be allowed to become parents? Should there be two parents, five parents, 10 parents, 100 parents? The point is, there has to be limits," he said.