Others have mentioned a lot of tools that can do this, but all of them are predicated on the accuracy of everyone's calendar. In certain situations, it's important to maintain your calendar in the context of a group's needs.
The first step is to make sure all appointments are up to date in all calendars. There will be a lot of rescheduling when certain members realize there was a meeting not entered.
Everyone should set boundaries on availability. Will this group adhere to business hours, or make evenings, weekends and holidays available?
You have to get everyone in the habit of always send meeting requests as a calendar appointment. Many people will put this in a plain email and never bother to check other calendars. Motiviation is difficult if some people don't keep their calendar up-to-date. These two things tend to feed off of one another.