In the episode “Always a Godmother, Never a God,” in reference to The Godfather.
RORY: I’m on my way over to Sookie’s kid’s baptism. I’m going to be Davey’s godmother.
LANE: Very religious. My mother would be impressed.
ZACK: Hey, is it true you get to keep the baby if the parents die?
RORY: I’m just doing it as a favor for Sookie.
BRIAN: Godmother, huh? (in an Italian accent) You make her an offer she couldn’t refuse?
It’s a cute allusion to The Godfather: Part I, where Michael describes how his father helped Johnny Fontaine get started in his singing career. He got Johnny a gig with a certain bandleader by offering the bandleader an offer he couldn’t refuse, namely, “Either your signature or your brains are going to be on the contract.”
Read more about The Godfather