Chet, the easiest way would have been to stain and finish the new pine before putting it up. Then all you have to do is a little touch up at butt joints including the miters.
It will be difficult to stain with the more common types of available stains because they contain mineral spirits/paint thinner that is a solvent for the glue on the back of most tape. You might be able to get by with a gel stain but a water soluble stain or analine dye would be a better choice. These are available at specialty woodworking stores and mail order houses.