I suggest that the main conflict in this play is the inner conflict of John Proctor. As a result of his extramarital affair with Abigail Williams, he "has come to regard himself as a kind of fraud." To the world, he presents the upstanding Christian, farmer, and citizen, but he knows that he has broken some of the most fundamental rules of Christian doctrine—injunctions against lying and adultery. His continued guilt and frustration at his wife for her perceived judgment of him clearly continues to plague him. He tells her, "Let you look sometimes for the goodness in me, and judge me not." She replies, "The magistrate sits in your heart that judges you."
It is clear that she is right, as, in the final act, when John has decided not to confess to a crime he did not commit in order to save his life, he says, "You have made your magic now, for now I do think I see some shred of goodness in John Proctor." He had lost sight of his own goodness, his own value, and he struggled all along to regain it; in the end, he finally does.
Ultimately, I'm not sure that John and Elizabeth Proctor really are in conflict. She is somewhat distrustful of him since his affair, and he is a bit embittered by her continued distrust, but they do love one another and seem to be trying to work through the challenges to their marriage. I think the conflict between Elizabeth and Abigail is of more significance in the play because Abigail wants John to herself so badly that she is willing to see Elizabeth hanged to accomplish it.