Solutions include:
1) Finding a window unit that has a decent "throw" of the air, this being the cheapest option available, it may not be as efficient, but the cost analysis really shows window units being the best price point. If you have it running all the time to maintain setpoint, it may behoove you to go for a more efficient method, but if you're only running it when someone is in there (and that isn't "all the time"), it turns out to be one of the most efficient methods on a cost basis, assuming of course it conditions the entire space. Cost: $300?
2) Extend ductwork, if your home system is oversized, this can be an option; to figure out if it is oversized though would require testing, or at least a calculation. This would require ductwork routing if it's capable to do so. back of hand test may help, how often does your AC Cycle (turns off and waits for temp change to turn back on) in the coldest/warmest (depending on climate)? If it often shuts down, it may be oversized enough to help. Old engineer method is ~300-400sqft for 12,000btu. (1 ton of cooling/heating) This method may or may not help, as it may be region specific, I tend to do Load Calculations to verify. Message me and we can chat about other options to determine if your system is right sized, or if you could make it oversized by doing things such as getting new windows, which would create enough difference to add in the new area. I don't know cost, contractor would have to really dig into it for a full evaluation.
3) Mini-Split system, You can place it in a different location central to the room to cover the whole room, Misubishi, Daikin, and a few others make them. This does cost a bit more, as it requires wiring, piping, but no ductwork, so if the ductwork renovation costs a bit, this may be a decent solution. They are very efficient with scroll compressors and fans that are not one-speed. you can then separate that room from the rest much like a window unit. It hangs on the wall for the cheaper ones, and I enjoy the design of them but some view it as an eyesore. There are ducted units that are less efficient but allow you to make in essence a new system out of them. A contractor told me this may cost ~$3,000 installed, but of course region specific and who you have available. Equipment ~1k, install ~2k. Estimated of course.
source: HVAC Building Design Engineer.