The Collaborative International Dictionary of English v.0.48:

Inconvincible \In`con*vin"ci*ble\, a. [L. inconvincibilis. See
   In- not, and Convince.]
   Not convincible; incapable of being convinced.
   [1913 Webster]

         None are so inconvincible as your half-witted people.
                                                  --Gov. of the
                                                  Tongue.
   [1913 Webster]

Moby Thesaurus II by Grady Ward, 1.0:

18 Moby Thesaurus words for "inconvincible":
   cautious, disinclined to believe, disposed to doubt, guarded,
   hard of belief, impervious to persuasion, incredulous, leery,
   shy of belief, skeptical, suspecting, suspicious, unconvincible,
   uncredulous, unpersuadable, unpersuasible, unwilling to accept,
   wary