Leslie:
You can certainly paint on the copper plates. There are two schools of process for painting on copper.
Both involve thouroughly cleaning the copper plate first with a copper cleaner like Bon Ami or steel wool to remove any oils or tarnish from the surface and get you down to the nice brushed metal.
Mechanical Bond
Because the copper is so very smooth, you need to rely on a combination of mechanical bond plus the chemical bond to make the paint adhere long term to the copper. A mechanical bond means that you scratch or abraid the surface so the paint laid over has nooks and crannys to dig into. The chemical bond will come from using resin in your medium - resin acts a lot like a very strong glue. The resin part is optional, but it will help if you use it.
The first method lets you paint directly on the bare copper and uses garlic as the ground, yes, garlic. Garlic is acidic and the juice from the garlic will eat into the copper etching it and helping to create that mechanical bond. You mince a bunch of fresh garlic up and wrap it in a cheesecloth and make a little bag out of it. You then mash the garlic with your fingers so the juice begins penetrating the bag. You will ponce your surface with the garlic juice and leave it on. When it is dry, you can paint on it with regular oils. It may help to use a medium that has some resin in it - something like venice turpentine or canada balsam. I like 1 part canada balsam to 2 parts stand oil to 1 part oil of spike lavender or good turpentine.
The second method involves using a traditional oil ground of either lead white or zinc white or a combination of the two. You can add one or more coats and paint as normal. Some recommend letting the primed panel sit for at least 3 months before painting on it. This method mostly or completely obscures the copper - I think that if you are going to paint on copper, don't you want it to show through in places? You will certainly get a very smooth surface with either method.
Hope that helps!