Buddy was probably allowed on the furniture where he lived before and doesn't understand the problem now.
From what you've described, I would say your dog is probably timid by nature. When you yell at him to down and he rolls over, he's not saying "look at me, I'm so cute". He is saying "please don't kill me!" That is also why he is dead weight, lying on his back, and peeing. These are signs dogs give to each other to indicate that they are lower in rank and submissive. The alpha dog recognizes these signs and leaves the more submissive one alone. You haven't left him alone and so by the time you get him to the corner, he is so very terrified, he has no idea what he has done! When you approach a timid dog this way, he will freeze up on you and nothing will get through.
A better solution would be to choose a different command than "down" (because to him it only means "lie down"). Perhaps use "off" instead. With a dog of this nature, you have to be very quiet and calm, never yell or use physical punishment. Try luring him off the couch with a dog cookie. Give the command as you lure him off, praise when he does it and reward him with the cookie.
You probably think he shouldn't be "rewarded" for doing something bad. He has no idea he's done something bad, so you're not rewarding him. He thinks he's being rewarded for getting off the couch, which is exactly right. With a timid dog, praise, food and quiet handling is the only way to go.
[This message has been edited by CarolineS (edited September 03, 1999).]