Ryan Gosling Is ‘Cherishing Every Minute’ with Daughter Esmeralda

01/21/2015 at 06:00 PM ET

Ryan Gosling Sings to Daughter
Dara Kushner/INF

Oh, to be Ryan Gosling‘s baby girl.

Since welcoming daughter Esmeralda Amada with longtime love Eva Mendes in September, the actor’s been busy flying back and forth between Los Angeles and Atlanta to shoot his upcoming film, The Nice Guys.

But that doesn’t mean the star hasn’t squeezed in as much quality time as possible with his family. “He’s been wanting to be a father for a long time,” a Gosling insider tells PEOPLE. “He’s cherishing every minute.”

Raising their daughter without a nanny, the new parents are “so tired, but so in love,” says a Mendes pal. “[The baby] is smiling and cooing and loves when Ryan sings to her.”

While Gosling, 34, and Mendes, 40, have no plans to wed any time soon, that doesn’t mean there’s trouble in paradise for the private pair, who stepped out for a rare date night on Saturday.

“Eva and Ryan are so happy,” says another source.

For more on Gosling and Mendes’s relationship and their plans for raising a family together, pick up the latest issue of PEOPLE, on newsstands everywhere Friday.

— Melody Chiu with reporting by Jennifer Garcia, Linda Marx and Aili Nahas

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