The aptly-named guard, Percy Wetmore, seems to be in conflict with everyone he encounters in The Green Mile. He is an outsider who makes no attempts to conform to the other guards' routine, but more importantly, he shows a cruel streak toward the prisoners. He takes pleasure in the death row inmates' miseries, and wants to experience pulling the switch to electrocute them himself. His greatest conflict, aside from with the guards, occurs with prisoner Eduard Delacroix and his pet mouse, Mr. Jingles. Percy stalks and finally smashes Mr. Jingles with his shoe, but the animal is resurrected by Coffey. Percy exacts his revenge by deliberately failing to dampen the sponge that conducts the electricity, leaving Delacroix to die slowly and in great pain.
I would say that the strongest example of interpersonal conflict exists in the very opening stages of the film. The entire system in which prisoner vs. guard is the dynamic that governs the penal system is something to which John Coffey forces reevaluation. The idea of the tension or conflict that exists between guards and prisoners is the pretext of the setting. It is also something that causes apprehension in the guards when Paul starts to tell them of Coffey's healing powers. When the Warden's wife is dying, the guards recognize that the need to break down this barrier of interpersonal conflict is the only way for healing. This healing is not merely for Hal's wife, Melinda, but also for themselves and their own way of perceiving reality. John Coffey's presence, then, is not only healing pain that exists, but helps to cause a fundamental change in the conflict that exists between guards and prisoners and how human beings can interact with one another, transcending beyond the social barriers that exist.