The Collaborative International Dictionary of English v.0.48:

Doily \Doi"ly\, n. [So called from the name of the dealer.]
   1. A kind of woolen stuff. [Obs.] "Some doily petticoats."
      --Dryden.
      [1913 Webster]

            A fool and a doily stuff, would now and then find
            days of grace, and be worn for variety. -- Congreve.
      [1913 Webster]

   2. A small napkin, used at table with the fruit, etc.; --
      commonly colored and fringed.
      [1913 Webster]