Get a seniority list of the reserves.
Go down the list so they reserves get the pick of what duties are available for the next week.
They should then in the interest of fairness...
Have the day off of the duty they are covering,if it's 'Bobs' duty and it's a Sat off then they have that.If 'Bob' was on it he would have that day off wouldn't he!
Get some kind of aggregate list,that way you can keep an eye on who's had Sat's off,if some,even if they are low on seniority in the list have not had a Sat off for a while then they get priority.