Communication, communication, communication. That's how you resolve these conflicting requirements. As a project manager, you are constantly faced with this situation, and you need to communicate with each and every stakeholder in order to reach a balance.
The best way to handle this is to hold a meeting that all the stakeholders will attend, and discuss each and every person's requirements in the meeting, and point out with whom requirements that stakeholder's requirements conflict with. At this point, stakeholders will do an extra effort to resolve the conflicts themselves, either by concessions or compromises.