If you live in the northern band of the country,
chances are the duct system was designed for heating.
Cooling requires more air flow than heating -
I suspect there is not enough air going to the upper rooms.
You should have two supply registers in each of the
One possible solution (not that easy, but possible) is
to run a 9" duct through a 1st floor closet to an area
behind the 2nd floor knee wall, then install a 9" x 6"
tee and run 6" duct to each room.
Also, make sure the ducts in the basement are sealed
with duct mastic.
You will most likely have to turn down the damper
during the winter, otherwise it will get too warm.
If that is not practical, look into ductless split system.
37 year HVAC professional