I need to buy new shutters for my shore home. The house is being newly painted and vinyl shutters do not come in the color I have chosen for the trim (doors and shutters. If I purchase vinyl shutters in, say - white - can they be painted in the same color as the doors and, if so, how do you do this?

There are paints that are specially formulated spray paints to paint plastics and there are additives that need to be added to laquer, because I have done both.

There is info here for painting plastic. How To Paint steel, Aluminum, Plastic, and Acrylic
Seems like a good surface prep and primer is necessary for latex.

I have worked at Lowe's in the Millwork dept for almost 12 years. Many of the colored shutters sold at Lowe's, HD or Menards now have a silicone base in the molded plastic. This will make painting very difficult. The shutter companies also make a paintable shutter so you can apply any oil or latex paint. These usually will need to be special ordered but some larger stores may stock them. This silicone base has been present for the past few years. Before you paint any of these, clean all surfaces with a degreaser. There will be mold release agent residue that will also hinder paint adhesion.

You can clean/degrease the shutter and pray on Rustoleums Universal paint or their plastic primer. After that, any good acrylic enamel or latex should be fine. Rustoleum presents Universal Paint • Welcome

Yes, that Universal paint sticks well to any surface. We painted some laminate bookshelves with it. I didn't figure it would hold up, but my wife really wanted to try that instead of resurfacing. She was right. It has really held up well.

You should probably clean with acetone or something similar. I would test a small area behind them first just to be sure the cleaner doesn't melt the plastic.
Al

Rust-oleum also makes a plastic primer which is much cheaper than their Universal which goes for about $6.50 a can. I used it on new stell clad doors that had vinyl trim around the windows. Worked great for me.