The Router Guys
Yes you can do it with the router if the baseboard profile is not to fine. You need to have a guide and a straight bit that fits into the guide. Next you need to make a pattern that is exactly the shape of the baseboard profile and a fixture to hold the baseboard in solid position during routing. How many of these cope cuts are you making? Hopefully more than two or three...to go further I need to see the profile, can you post a photo?