I'm pretty sure that the green patina coating is copper sulphate. Go to a plumbing store and get a bottle of sulfuric acid. (Read the label closely and make sure it's not hydrochloric acid acid (aka muriatic acid) and also of course make sure its not sodium hydroxide (lye)). Here locally, ACE hardware does sell sulfuric acid in it's plumbing section.
Get some sulfuric acid and dilute it and paint it on your copper. Warning: If you have a bowl, do not fill it with sulfuric acid and then add water. Fill a bowl with water and slowly add a little sulfuric acid.
When sulfuric acid goes into solution with water, it generates tremendous heat. If you drop a few drops of water onto pure sulfuric acid, the water droplets will immediately boil and turn to steam and possibly erupt into your face.
.....Another sulfuric story. About four months ago, I wanted to derust a differential crossmember. In the past I've used vinegar, but it's expensive and slow (although quite effective). I bought large plastic trashcan and filled it up with water and sulfuric acid. In went the crossmember (dunk). In doing this, I didn't seem to get fast enough results, so I added more sulfuric acid. Leaning over into the trashcan and lifting up the crossmember to check on it's status, my eyes were stung by sulfuric acid fumes. Actually more than once. Anyhow, it damaged the mucus membranes inside my eyelids. I had a lot of eye discomfort and used eye drops (saline) for quite some time. Just now I think the problem has gone away. I did derust the crossmember. Now ...how to get rid of the sulfuric solution??? I wanted to just pour it in the street, but I had to neutralize the acid. I started adding Ace hardware sodium hydroxide. It really wasn't strong enough. I ended up going to Home Depot and buying their sodium hydroxide(NaOH). Adding NaOH to surpheric acid (H2SO4) to get a pH of 7.0 was tricky. At first, I added NaOH and got a pH reading of maybe 8, then I added a little more H2SO4 and got a pH of 5.5, etc. Getting a pH of close to 7.0 was a real problem. I finally got there and dumped the stuff. I think in the future, I'll stick to vinegar (acetic acid). Its slow and expensive but it's trouble free to get rid of. Oh, by the way. if you're going with vinegar, go to the grocery store and check out 10 gallons of vinegar, you'll get some strange looks.