At almost any hardware store or Lowes and Home Depot carry paints that are directed specifically for coating vinyl and other surfaces. Unfortunately spray paint doesn't tend to stick to vinyl very well. When applied with a brush it can be quite a timely task but after a few coats, the result is great. The Ideal way would be with a good powered sprayer since the shutters most times are removed...but I've painted shutters while they're still hanging and I use a long painters blade to slide between the siding and shutter, then brush it lightly. The first coat looks terrible, then it all comes together during following applications. You have to kinda jam the brush into the corners of the louvres that's the hardest part, lol. The result is worth it.
Most savvy painters know that painting vinyl shutters is not only a hassle, but can also be extremely messy. Most homeowners are inclined towards using paint brush for this but that can be extremely time consuming and if you are not lucky you are likely to be left with drips, streaks, and runs. You can use the Krylon sprayer if you want it to be faster. You should also ensure that your shutters is paintable because if not, it will run after a time.
But yes, you can still do it, you can repaint plastic or your vinyl shutters. The first step is to determine if they are new or not and then asking the manufacturer is there is going to be a special cleaning that is needed after which you follow their painting instructions. However, if they are not new and have been taking dust for some time, you have to do a good cleaning because you start to paint it.
You can kill mildew or mold with a mixture of one part bleach to four parts water in a pump up garden sprayer or spray bottle. You then have to rinse completely with a hose. This extra step is needed when they are present. And if they are not present, then you don’t need to do this at all. When working with bleach, make sure you have protective cover to prevent contact with your eyes, skin, and plants that may be around.
The next step is to clean out dirt or chalking on the shutters by scrubbing with detergent and water. After it’s clean, rinse off with a hose and allow them to dry completely before you paint.
You have to ensure you use high quality exterior or acrylic latex when painting your vinyl shutters. Or if you are painting plastic, you should go with a paint that is just designed to paint plastic. You can also increase the adhesion and allow better coverage by the top coat when you prime the shutters with a latex primer. This is optional and is not required to paint vinyl shutters. But if I were you, I would do it since it will have a long lasting effect and you will be proud of the job after you are done. One thing you should avoid totally is painting the shutters darker colors that they were originally. The reason for this is that the surface is going to absorb more heat this way and since it is not designed for this, it might quickly warp and that is not what you want.