Scheduling Staff is usually handled by internal calendars or event management systems (i.e. EMS).
But how do you schedule volunteers? Why not devise a calendar system on the Church web site that would let volunteers schedule themselves for various tasks. You would assign each volunteer a set of roles, e.g. sound technician. They could then look at the calendar and pick the days that they are available to run sound. The calendar system would then keep track of the fact that they had volunteered to run the sound desk on the particular date. If they needed to change, the system would allow them to drop that commitment of time and post the task back to the available tasks pool. Another volunteer trained in sound could then volunteer online to take their place. You might need a hot list of items that were coming up, so that volunteers accessing the calendar would see what was most needed. Overall, this would take care of scheduling volunteers for technical ministry tasks automatically.

Does such a system exist? Perhaps, but it would need to be flexible and role based. If you know of such a system, then please comment below so that others can discover it.