Funny, but is it necessarily something to be concerned about? Is there a lot of eccentric stress walking down stairs, even while carrying weight? I don't know - I'm asking an honest question here.
If walking down with weight is a problem, you can try this: find a hill with some heavy rocks nearby. Carry a rock up the hill. Leave the rock on top of the hill, walk back down. Yes, you might have some eccentric stress walking down, but it will just be your bodyweight. Eventually you may run out of rocks. At that point, start rolling the rocks back down. If you can't find big rocks, make a sand bag out of a round duffel bag - an old Army duffel will work well. Carry the bag up the hill, roll it back down. If you don't have a hill nearby, then I feel sorry for you.
Here are a couple more:
Ride a bike up a hill in a big gear. Cycling, in general, is eccentric-less. The problem is that the resistance is very minimal, unless you ride up a big hill in a big gear.
For the upper body: Swim sprints.