The Collaborative International Dictionary of English v.0.48:

Unappealable \Un`ap*peal"a*ble\, a.
   1. Not appealable; that can not be carried to a higher
      tribunal by appeal; as, an unappealable suit or action.
      [1913 Webster]

   2. Not to be appealed from; -- said of a judge or a judgment
      that can not be overruled.
      [1913 Webster]

            The infallible, unappealable Judge [God]. --South.
      [1913 Webster]

            We submitted to a galling yet unappealable
            necessity.                            --Shelley.
      [1913 Webster] -- Un`ap*peal"a*bly, adv.
      [1913 Webster]

WordNet (r) 3.0 (2006):

unappealable
    adj 1: not subject to appeal; "the judge's ruling was handed
           down in a preliminary hearing rather than a trial and was
           therefore unappealable" [ant: appealable]