The Collaborative International Dictionary of English v.0.48:

Tidy \Ti"dy\, n.; pl. Tidies.
   1. A cover, often of tatting, drawn work, or other ornamental
      work, for the back of a chair, the arms of a sofa, or the
      like.
      [1913 Webster]

   2. A child's pinafore. [Prov. Eng.] --Wright.
      [1913 Webster]