EMILY: We have a couple of wonderful writing desks, and some French end tables, rocking chairs, picture frames, lamps, davenports.
Originally, davenport was the name given to sofas made by the furniture makers A.H. Davenport and Company, from Cambridge, Massachusetts. It sold luxury furniture through its showrooms in Boston and New York City in the 19th and early 20th centuries, and made furniture for the White House. They ceased business in 1974.
The word is now used for a rather confusing number of sofa types in the US. It may mean a boxy formal upholstered sofa, like the ones originally made by Davenport, or a sofa which converts into a bed, or a futon-style sofa with storage underneath it, or just a generic word for a large high-end sofa. I’m not actually sure in which sense Emily is using it, but I think either the first or the last is the most likely.
As an extra layer of confusion, a davenport is also a 19th century English word for a small writing desk, but as Emily already mentions writing desks as separate possibilities, I think this one can safely be ruled out.
The Annotated Gilmore Girls 