Either offers uniquely different visual elements that you can bring into your projects and both are simple enough that anyone can do it.
Spray Paint
Buy spray paint that is meant to stick to metal surfaces. For metal art projects that will go through a lot of handling, it is also advisable to scuff the surface lightly with sandpaper to remove the shine and coat the copper wire with a primer before applying the color coat.
Do these steps in a well-ventilated area, and cover any surrounding surfaces with newspaper or plastic to prevent damage from over-spray. Spray in even, light strokes, allowing each side to dry thoroughly before turning another side face up to be sprayed. Coat it with a clear coat sealer for extra staying power.
Hand Painted
Using a small brush and metal craft paint to add small designs is the easiest way to color copper wire that needs a more elaborate appearance. For example, paint the entire wire one base color and then add swirls or stripes around it in another hue for metal art projects.
Use a primer to ensure that the topcoats stick. A trick to ensuring an even coat is to drill a few tiny holes into a block of wood, just large enough for the end of the wire to be stuck in. This allows for more flexibility when hand painting. Allow it to dry thoroughly before turning it around and coating the small end that was hidden. Spray it with a clear coat sealer for extra durability.
Heat
The easiest way to color copper wire and keep the originality of the material is to use heat to naturally patina it for metal art crafts. This method creates beautiful hues of greens, browns and even pinks and purples depending on the purity and density of the wire itself.
Secure the wire in place with a block of wood with small holes drilled in it or a clamp off of the edge of a table to avoid being burned, as the entire piece will get hot very quickly. If you choose to hold the wire while heating it, wear heat-resistant gloves. Take a lighter and run the flame up and down the wire (the flame of a candle also works well if you are holding the wire), twisting and turning it to create swirls and other designs.
Seal it with clear coat to keep the hues. This is the easiest way to color copper wire where no two metal art projects will be exactly alike.