If there are only a few missionaries who do scheduling, you can add them as out-of-unit members, which will allow them to see the stake calendar and directory. If things haven't changed in the past few years, the easiest way to add an out-of-unit member at the stake level is to go to Callings by Organization, find an appropriate standard calling (maybe something under activities, service missionaries, or facilities), and type their membership record number in the auto-complete box where you would normally type a name.
As another route to look into, the stake calendar administrator manages the list of units that can schedule the buildings assigned to the stake. The system is flexible enough that, for example, wards from other stakes can be added to a building. I'm not sure if a mission can be added to a building, but if the missionaries are organized under a standard mission, it's worth checking with the stake calendar administrator (usually the stake clerk or executive secretary) to see if the mission shows up in the auto-complete list of units for the building.
Another option is calling a stake building scheduler and assigning them to work with the missionaries for scheduling their events.
Samuel Bradshaw • If you desire to serve God, you are called to the work.