Usually in all two story homes the duct system to the second floor is inadequate. This is probably your main problem to start with. You might try and adjust any dampers (if you have them on the ducts) to force more air to the second floor but if the return air duct is not large enough or installed to scrub the hot air off the ceiling area of the room even that will not be of great help.
You can thank the original builder of the home for this since older homes were not designed for A/C to start with and the newer homes do not get the extra money spent on HVAC duct work since the ladies like the fancier kitchen cabinets and floors so that is where the new home builders spend the duct work money instead.
The new home builders motto is make it look good to sell the house. No one cares about how the HVAC duct looks because it is hidden in the basement or behind the wall.
You might have a local professional do an ON SITE survey of your problem since it is just about impossible to see your duct system from here.