Consider this the coloring book version of applying a black and white or "antique" filter, as you would do on your Instagram feed. Working in pencil, marker or paint, choose a neutral palette. As you can see on the top image, shading with regular pencil on your coloring book image makes it look less like a coloring book image, and more like a hand drawing. By using a palette of browns, you can create an "antiqued" look on your coloring book pages, as if they are treasures from a different era.
When you are coloring, make sure you have a good light source so that you aren't straining your eyes. During the day try and find yourself a nice spot by a window with plenty of natural light, alternatively invest in a daylight LED lamp so that you can have a decent bright light to color under day and night. Some of these lamps even have in_built magnifying glasses which will help you when coloring detailed pages, but will also put less strain on your eyes.