Check your registers on the upper floor and see if they are closed. If you have the floor or ceiling vents closed or partially closed, then the maximum amount of cool air cannot circulate upstairs. The colder air will sink to the lower floor, so you will want to make sure you are pumping as much chilled air upstairs as possible. Also make sure you have no furniture sitting on top of the vents. This is no different from closing them altogether.
There are levers located on your ducts that control the amount of air that is allowed through a particular airway. These air dampers can drastically change the temperature level in different parts of the house. Try opening the dampers that lead to the upper floor of your house all the way if they are not already open. If you do not know how to access your dampers, contact an HVAC repair technician to do it for you.
Install Return Air
Install a return air system on the upper floors of your home. This is a considerable project, but it will make cooling your upstairs areas much easier. Since the warmest air in the house gathers near the upstairs ceiling, the return air vents should be placed near the ceiling to suck in the hot air and recirculate it through the cooling system. Without it, you will continue to experience warmer temperatures upstairs, most likely as the heavy cool air sinks to the floor and trickles down stairwells to the lower level.
If your second floor has its own unit for cooling, then it has little to do with sinking and rising air; it is a problem with the unit itself. Check it for typical problems to find out why it isn't cooling. It could have a refrigerant leak, iced condenser coils, a dirty filter or a mechanical problem. A checkup from an HVAC specialist should be able to pinpoint such problems in your upstairs air conditioning unit.