LUKE: Randy and Barbara don’t wanna miss their brat kid’s rugby semifinal … My sister never even called back. My cousins Paul and Jim, who my dad helped put through college, said they were too exhausted from a fishing trip. And slightly disturbed cousin Franny said she can’t leave because her Petey’s sick.
Randy and Barbara, a married couple with at least one child, who plays rugby, not sure whether Randy or Barbara is Luke’s cousin.
Liz, Luke’s sister
Paul and Jim, cousins, presumably brothers
Franny, cousin, possibly a sister to Paul and Jim? (and yet another Fran/Francine/Franny!)
Uncle Louie didn’t have any children, but Luke seems to have several cousins, although he doesn’t mention any other uncles or aunts. Perhaps they are already dead. It’s possible all the cousins mentioned are siblings, and only one uncle/aunt died before Louie.
Luke booked nine rooms at the Independence Inn for his family to attend Louie’s funeral. He only seems to have needed five rooms for the named family members, suggesting that the other four were for the unnamed relatives who said they couldn’t get out of work for the funeral.
The Annotated Gilmore Girls 