Ho trovato questa frase per esempio
“Come away from there, Mac,” said Catherine. “Do not drool on my gowns. Come and lie here on your blanket, there’s a good lad.” She managed to coax him away from the trunks with the help of a good fire in the sitting-room.
It's something you say to a young boy to reassure him that he's doing the right thing or to complement him for doing well. SOmething like '"Aren't you a good boy!" or in this case "Be a good boy and come lie down here." I think Fai il bravo ragazzo sounds about right.