Rances, 26, gave birth to Crisostomo Manuel at 9:45 a.m. yesterday by Caesarean section, The STAR sources said.
"The boy is healthy. He has no physical defect," said a source close to the Rances family.
The source refused to disclose Rances location, but said she was resting after delivering her second child with Yalung, 49. He is now a librarian in the US after leaving the Philippines last November in the wake of the scandal spawned by the disclosure of his first child with Rances.
The second child was reportedly conceived in September, or three months after the birth of their first baby, a girl, in June.
Earlier, Rances had claimed that Yalung was aware of fathering another child. She said she was seeking support for their two children.
Meanwhile, Rances told ANC TVs "Strictly Politics" aired Tuesday evening that she may go to court in a bid to seek child support from the local Catholic Church.
Rances threatened to raise the issue of "child abandonment" against Yalung if her appeals for financial support were ignored. She said, however, that she had not yet determined from which particular diocese she would seek financial support.
Rances suggested that she intended to file the suit to disprove allegations that she benefited from the local Catholic Churchs funds.
Rances claimed that Yalung left her a "letter of stewardship" for the P6-million trust fund that the former bishop had deposited in a bank under his name.
She said the letter was given to her before Yalung left for the US.
Insisting that she has not availed herself of the money, Rances said, "My sufferings have been great and we have no money. I want to clarify ... that I have never received a single cent from the Catholic Church as support for anything."
She said the P6-million trust fund was "not enough for even a year of support to my children" even if she had access to it. With a report from Ann Corvera