The Collaborative International Dictionary of English v.0.48:

Sunshade \Sun"shade`\, n.
   Anything used as a protection from the sun's rays.
   Specifically:
   (a) A small parasol.
   (b) An awning.
       [1913 Webster]

WordNet (r) 3.0 (2006):

sunshade
    n 1: a canopy made of canvas to shelter people or things from
         rain or sun [syn: awning, sunshade, sunblind]
    2: a handheld collapsible source of shade [syn: parasol,
       sunshade]

Moby Thesaurus II by Grady Ward, 1.0:

19 Moby Thesaurus words for "sunshade":
   awning, beach umbrella, blind, brolly, bumbershoot, cover, curtain,
   drape, drapery, gamp, light shield, parasol, screen, shade, shader,
   shadow, sunblind, umbrella, veil