Updated with solution
I was going to edit my first post, put this info in there, and put "UPDATED" in the title, so that anyone with the same problem can easily find the solution, but after a certain amount of time, you can't edit a post, so if a mod sees this, please add this post to my original post.
I checked out the colorbond website that Jomax listed. That company is "factory approved" by Ford, so if you've got a Ford, you can look up the exact paint color by the trim code of your vehicle. Unfortunately, at the time of this writing, you can't look up Toyota colors by trim code. You just have to look at your trim, then look at the computer screen and try to pick a color that matches. Seems to me that I would have to get incredibly lucky to match it up without having the actual product in front of me.
I went to a local paint supply store that supplies body shops. They had the same type of product- vinyl trim paint in a spray can- but manufactured by SEM. They had tons of different colors in stock.
I had removed the airbag cover and brought it with me. We picked out several different colors that looked close, then took them outside and
sprayed several different sheets of cardboard to find the perfect match.
I took it home, cleaned the cover, and sprayed it. When I reinstalled it, it didn't match up at all. I went back to the paint shop and tried another shade.
The second shade worked perfect. It is literally a 99% match. A professional painter would notice the slight difference. A professional detailer might notice. But the average man on the street will never notice. If I point out the difference you can look at it and see a slight variation, but not unless I point it out.
Important Points
If you don't prep the surface really well, the paint will start coming off in a relatively short amount of time. I cleaned with soap. Then I kind of gently roughed up the surface with a scouring pad to give the paint a little bit of a rough surface to adhere to. Cleaned with soap again. GENTLY cleaned with a 5 to 1 water to 91% IPA mix, then washed with Dawn again. You MUST get all the old dressing off.
If you don't have a lot of experience painting, you'll definitely want to take the piece out of the car.
The underlying color of the surface you're painting WILL affect the final color. This was my problem with the first attempt. It looked like a perfect match when applied on a white cardboard sheet, but when I put it on the darker colored plastic, it ended up too dark.
Spray from 10 inches away. It will seem like you're too close, but you're not. If you get too far away, the paint droplets don't atomize right. They gather together into bigger droplets and don't lay down properly and the finished product looks horrible.
MULTIPLE LIGHT COATS! If you put it down to heavy, it'll look splotchy and be impossible for an amateur (like me) to blend. Let each coat get dry (but not cured) before putting on another coat. Anywhere from 5-15 minutes between coats, depending on temp, humidity, and how thick you're laying it down. If it still looks shiny/wet wait a little longer before putting another coat down.
Once it's dry, let it cure as long as you can before reinstalling it. The last thing you want to do is to rub some of the paint off when reinstalling it.
I am a complete amateur when it comes to painting, but this is the process that worked for me.