Opposite words for convince:
dissuade, deter, unsell, hold back, restrain, hinder, repel, discourage.
Usage samples:
  1. " Well, it is true; and you have only to come to Mr. Boyd's to convince yourself of the truth.
    "Little Miss Joy", Emma Marshall.
  2. I can convince you in a few words.
    "The Last Hope", Henry Seton Merriman.
  3. This picture will convince you."
    "The Prophetic Camera", John McGreevey.
  4. All this may appear very absurd; but a little reflection will convince the reader to the contrary.
    "Newton Forster", Frederick Marryat.