The smallest ducted system is 1.5 ton, which is about twice the capacity you need. If you don't want to stump up for a minisplit, you could use a window unit (probably a non-starter) or tap into your existing system. Depending on how big it is (preferably 3 ton or larger), it should work if done properly.

Before concluding that your existing system isn't capable of conditioning the addition, some ACCA Manual J calculations are in order as is an assessment of the existing ductwork system. An investment in sealing your existing ductwork system might provide the incremental capacity you need.

For such a small space I think I would pick an inverter window unit like this new saddle shape from Midea.

It's an inverter they start out in 8k btu go up to 12k btu (1 ton is 12k btu)

I think the 8k btu model would be more than enough for 300 sq ft. / You could run or have a heat load performed to make sure.... even over sized a little bit, the inverter operation will take care of it as these are load matching machines.

When it breaks you go out and buy a new one. There's only a year warranty on it, so if you don't maintain it -- it probably won't last long.

For such a small space pretty much anything you buy will be over sized. Over sizing leads to mold most of the time.

It would be premature to prescribe a solution without more information. If you live in a neighborhood with a homeowners' association, check whether your HOA permits installation of window units before going that route.

Thanks for the replies. I’ll be sure to revisit tapping into existing system capacity before moving forward.