The Collaborative International Dictionary of English v.0.48:

Convincible \Con*vin"ci*ble\, a.
   1. Capable of being convinced or won over.
      [1913 Webster]

   2. Capable of being confuted and disproved by argument;
      refutable. [Obs.] --Sir T. Browne.
      [1913 Webster]

WordNet (r) 3.0 (2006):

convincible
    adj 1: being susceptible to persuasion [syn: convincible,
           persuadable, persuasible, suasible]