What does Proctor tell Danforth about his doubts?
Here are some of the direct quotes:
Excellency, does it not strike upon you that so many of these women have lived so long with such upright reputation, and -
It's interesting the way he puts this because he shows respect, but frames it in a question so that the almighty judge must think about it. Proctor gets cut off by Parris who questions his faith.
In reference specifically to Rebecca Nurse he claims this about who is speaking:
It is children only, and this one [referring to Mary Warren] will swear she lied to you.
Proctor doesn't have doubts about what is going on. He does know truth, but he is trying to present Danforth with reasonable evidence to give Danforth doubt with what the girls are saying.
He further tries to give Danforth reason to doubt by providing a list of names who support and claim the women accused are of good virtue.
I think that you are talking about the conflict between John Proctor and Danforth in Act III, Scene 1. There are two things that I see there that you might call doubts.
First of all, Proctor believes that the girls (Abigail and her gang) are making up all their accusations. I am not really sure that you can call this a doubt, though. He knows in his heat that the accusations are false so I don't think of it as a doubt.
Second, and very closely connected to the first, Proctor does not believe that God is saying that Rebecca Nurse is a witch. He thinks it is only the girls. So he is doubting that God approves of the way the trials are going.