Without adequate insulation and ventilation it is easy to create a hot box. With enough windows in the right location you can have it just right and still have a hot room.

There are really 3 options:

1. Shade the structure
2. Insulate and ventilate the structure
3. Blast it with cold air.

Perhaps a large shade or series of shades on the outside attached to you soffit (south or west wall maybe) to block sunlight from coming in, shading multiple windows and the wall unit at one time. Lower in high sun times, raise at others. Or some type of shutters like you see at the beach. Window tint might help too.

Plant some fast growing ornamental shade trees to block some light.

Better windows: double pane, gas filled, insulated.

Better insulation R factor in attic space (if you have one), walls and ceiling, if possible, depending on construction. Spray foam might be a good application in this setting.

Depending on roof and ceiling construction, consider adding some roof venting (turbine, power fan, ridge vent) along with good soffit venting ratio, if possible.

That along with a window unit should help. From an efficiency standpoint, if you have adequate shade and insulation/ventilation, then the air unit will not have to work as hard for as long to have the room at least satisfactorily comfortable.