Most human beings want to make sure things work well and that all is fair for everyone (I say most because there are always the egoist, the bad, and the idiot). In any case, the best way to get the employees on your side and have them make reasonable requests is to share as much information as possible.
Since you are establishing your schedule against a defined workload, you need to share that workload with the employees. If they see how many people are required each day, they are less likely to complain because they’ll know why they are scheduled at that time or on that day. They will see their contribution to the workload you measure as a planner.
If you have established fair rules like counting Sundays worked so that everyone works the same number of Sundays, make that number public with the schedule. People will see when they are scheduled for a Sunday that it is actually their turn and that everyone else has more Sundays worked.
This also has the effect of balancing dynamics. Peer pressure amongst the group will establish a sense of justice and fairness since everything is public. If someone calls sick on Sundays all the time when their turn comes, there will be a low number of Sundays worked that will be next to their name. That person has exposed themselves to comments from the others on the team. Obviously, this is a double-edged sword. The details on how you count these Sundays will either improve that sense of justice or make it worse. If you decide to count only the worked Sundays, then someone going on vacation will be penalized negatively. Also, if someone decides to use all their vacation so they don’t work on Sundays, so be it. But that fairness number then needs to include paid vacation (but not sick calls) for example.
So the numbers you decide to make public need to be there to help communicate your decisions as a planner. The goal is to inform the employees on what you do and how you do it. It reduces the sense of injustice some may feel, it will definitely reduce the questions the planner gets every time a schedule is posted, and it also empowers employees with the scheduling problem. If they can see another solution, they may bring it to you.
With this information, employees will make shift swaps on their own. You need to make sure, as a planner, that you display the required skill set you measure when you schedule so that employees can determine if that trade is good or not.