Creating an "every-other-weekend" staffing schedule is a relatively simple calculation that can be incredibly complicated to implement on a human level. The key is to make the process transparent, and allow your staff to have a say in the final schedule. As long as everyone understands that the assignment of weekend work was fair and balanced, there will be minimal opposition to the new calendar. Be sure to create a system to allow for some flexibility as well in case of illness or unexpected family obligations.
Calculate the number of working weekends your organisation requires in a year. Begin your calculation from a logical date such as the first of the next month, or the financial year.
Assign a single point to each working day on the weekend. Assuming your organisation is open year-round, this will be a total of 104 points (one for each day of 52 weekends a year). You may assign double points to long weekends (e.g. Labor Day) or holidays (Christmas).
Consult with your staff to find out if they have any specific requests, for example if they plan to request vacation time in a particular month. It's important for employee morale that you involve them in the process rather than unilaterally dictating their schedule.
Allow employees to volunteer to take holidays and long weekends for additional points. Many employees, particularly those without family responsibilities, may prefer to work those times to earn more weekends off during the year.
Pencil all the employee requested times in a calendar, then assign all other weekends to staff on rotating basis. If you're working with two employees (or teams) who alternate weekends, each employee (team) will begin with an assigned base of 52 points. Calculate all the points earned by each staff member (including the bonus points for long weekends and holidays), and adjust accordingly to fairly distribute the assignments.
Present the final schedule to your staff for confirmation.
This system will also work with more than two employees or teams. Simply divide the total points by the number of staff who will be assigned to work on weekends. For example, if you have 52 weekends with one point each for Saturday and Sunday, that makes 104 points. If you have a staff of 4, then each staff member will be required to fulfil 26 points worth of working weekends or holidays.