How do I paint PVC decorative backsplash panels?

Depending on the top texture, you may have to lightly sand to rough up the surface so it will hold paint. If its not smooth or shiny, priming it before paint may work

I'd mask off area so you can spray paint them with spray paint made for plastic.

Like Dianacirce70 suggests. Use a green kitchen scrubby to remove any shine. Prime with Kilz primer then paint your color.

Hi. Clean well and use wet sand paper (it is used for wet sanding metals, plastic, fiberglass) lightly. Use a spray bottle of water that has a fine mist. Clean with tack cloth. Use a primer for plastic, then use artists oil paints. Happy DIY'ing!