Where I live, everyone has central AC. I don't even know of any neighborhoods that even allow window units. AC is a core part of surviving here. Our heat index has been well over 100 almost every day since before May ended.
As far as super cooling a room, it all depends. A central AC has to be balanced. This is typically done by having more or fewer vents, larger or smaller vents, and where you place the return air ducts. If your AC company is good, you can tell them what you want and they can do it.
If you want to get really fancy, they make systems that allow you to set the temps separately in different zones or rooms. With that, you could adjust your room to whatever temp you want. Those systems aren't popular, so I assume that they are either expensive, don't work very well, or both.
I would also advise that you get a programmable thermostat. During the school year, I let the upstairs get much warmer during the day since no one is up there. The savings are even better for families that entirely leave their house during the day.
Also, if you have a two story house, you might consider getting two units. The heat load is very different upstairs vs downstairs. On the other hand, if you are an area where AC is a luxury, that might be overkill. Down here, if you have a two story with dual zones, you have to put up with annoying temperature differentials between the floors.