Call your dealer and find out who they use. Chances are they don't do paint inhouse, and they will probably give you the contact info for the people they farm paint out to. Call them, get a price quote, it might be a lot cheaper than you think.
As for doing it yourself, if you don't have a proper air compressor then rattle cans are your only option. It's possible to make it look good, but it takes a bit of patience. Find the paint code Suzuki supplies for the color you want and google it. I'll bet duplicolor will end up having something that matches, but you can occasionally find OEM paint in a spray can. It can be expensive though. Honda's 'Asphalt Black' costs over $100/qt.
Once you've picked your paint the fun begins. Wash the parts, then comes the sanding. You want to sand 3 times (more or less) with progressively finer sand paper. Say, 200, 600, then 1200, washing it off in between. Wet sand it if you can. Then put a coat of paint on it, 200 sandpaper, paint, 600 sandpaper, paint, 1200 sandpaper, wet sanding if possible, if not wash/rinse the parts between sanding and painting. Once you've got several layers built up, drying in between, then you clear coat it. You follow the same process with the clear as with the color. If you use a spray can you might have to put 2 coats between sanding (its REALLY thin,) and you may need to spend some more time sanding to get rid of runs. All of this needs to be done in as dust-free an environment as possible.
You'll also want to find a clearcoat that doesn't need to be baked on. Most do in order to get the hard shell-like finish that will protect the paint. Don't expect to finish in a day. Hell, I wouldn't expect to finish in a week tbh.