Miller definitely portrays the two men as not truly believing in the veracity of the girls' testimonies. In Act 4, Rev. Parris is just as John Proctor described him--"a broken minister." He cares more about his money being stolen by Abigail than he does about his having a part in the sham trials. While he does try to influence Danforth to postpone the hangings, that is more to assuage his guilt than anything else. However, the fact that he is concerned that townspeople who are respected members of the community are slated to be executed and tries to stop that illustrates that he doubts the validity of the judges' and his own actions.
Danforth is too intelligent and cunning to believe that he is actually sentencing guilty people to death. However, he will not humble himself or relinquish the immense power that he has gained to spare the lives of a few townspeople. He is willing to allow John Proctor to make a false confession so that he can spare him and still look logical to the town. He tells Hale and Herrick that
" 'Postponement now speaks a floundering on my part; reprieve or pardon must cast doubt upon the guilt of them that died till now' " (Act 4).
Danforth obviously knows that he is too embroiled in Salem's issues to back out, and thus, goes through with the executions.
While I think both men knew that the trials caused the deaths of innocent people, Miller's characterization of them does lead the audience to suspect that they would ever admit to others or even to themselves that they were guilty of evil acts. Both are too self-serving to do so. On a historical note, Rev. Hale is the only participating leader in the trials who apologized for his part in the Salem trials.