Courteney Cox Welcomes a Baby Girl

06/13/2004 at 02:00 PM EDT

Courteney Cox Welcomes a Baby Girl
Jean-Paul Aussenard/WireImage
Courteney Cox and David Arquette are parents at last. The former Friends star gave birth to a girl Sunday morning, sources told PEOPLE.

Cox, who turns 40 on Tuesday, checked into a Los Angeles hospital about noon on Saturday. She was in labor all day and overnight. The baby, named Coco, was born about a week before the scheduled due date.

"Courteney and her baby are fine," a source who spoke with Cox this afternoon told PEOPLE.

After years of struggle to have a baby, the couple announced the pregnancy last January. "I'm gonna have a ton of fun being a dad," Arquette recently told PEOPLE. "I can't wait to read stories and play games and the whole thing."

Arquette, 32, and Cox, who married in 1999, candidly discussed their attempts to become parents, with Cox saying last October: "I get pregnant pretty easily, but I have a hard time keeping them."

Despite having miscarried "quite a few times," Cox told PEOPLE, she and Arquette "bounce back pretty quickly. I don't say it's a walk in the park. But what are you going to do? We just try again."

Their first round of in vitro fertilization was "nerve-racking," said Arquette. His usual playful spirit could not block the frustration and tears after each miscarriage. "I feel terrible that she has to go through so much."

At the time, the couple was even said to be cautiously optimistic about trying in vitro fertilization again.

"It's a fact that after a certain age you have less of a chance," said Cox, who, along with Arquette, reportedly was not ready to discuss possibilities such as surrogacy or adopting.

Cox just wrapped up the 10th and final season of Friends. She met Arquette, the youngest member of the famous acting clan – with older siblings Rosanna, Patricia, Richmond and Alexis – on the set of the 1996 movie Scream. The couple are co-producers of their show on the DIY channel, Mix It Up.

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