How do I properly size an air conditioner for a very sunny room?
This page from Energy Star gives some good basic guidelines.


  
  If the room is heavily shaded, reduce capacity by 10 percent.
  If the room is very sunny, increase capacity by 10 percent.
  If more than two people regularly occupy the room, add 600 BTUs for each additional person.
  If the unit is used in a kitchen, increase capacity by 4,000 BTUs.
  Consider where you install the unit. If you are mounting an air conditioner near the corner of a room, look for a unit that can send
  the airflow in the right direction.
  


I'd say your room fits the "very sunny" definition.