need to cool room
Is there any air coming out of this register and if so how much? Don't assume that there is air or enough cfm coming out. Unfortunately, when systems are installed, the venting is either undersized or pulled off of a trunk line that is either too small or already over loaded. Is the ducting in your attic 'insulated hard-duct' or is it flex duct, which builders use because it is quicker and cheaper to install. One of the things that most designers overlook is the physical capabilities of the ducting itself.
Hard-duct (metal) has twice the airflow capability than flex duct of the same size. It is unfortunately assumed that they are the same. Also, the ducting needs to be the proper size for the 'cubic feet' of the room. When you have a vaulted ceiling in a room, it adds an additional "conditioning requirement" to the air exchange load of that given space. Most A/C contractors only go by 'square feet' when calculating and not by 'cubic feet'. Also, if you have 'flex-duct' make sure that the runs are as straight and bend free as possible.
Question - do you have a return vent in this room separate from the main return, which is probable in a hallway or some other part of your home? Proper air cycling thru your HVAC system is the key to conditioning any and all of your home. If the return is too far away the vaulted ceiling, the vaulted ceiling space acts as a heat storage space, and unless this heat is removed, even upsizing your supply will not solve your problem.
Assuming (I hate this word) that the equipment was properly size for your home - either 400 sqft or 500 sqft per ton of cooling - (taking into account any and all vaulted spaces, proper duct sizing, windows and their size & location, insulation, etc.), installing a ceiling fan in your room may help with this problem, as it will help move the trapped heat load down and back to the return. (assuming, it is not to far away or blocked by doorways or turns in your floorplan.)
Unfortuneately, your situation is all too common, because many designers don't really have a full understanding of how important proper air exchange and flow thru a home makes a home comfortable and keeps any system, no matter what the SEER rating is, working properly at peak performace.
Hope you get this resolve soon!
mac in lakeside