As an owner of a dog that had some fear issues (not due to abuse, he was born with a tendency to fear-aggression as both his parents were fear-aggressive to strangers) I can sympathize!
The key is what trainers call "desensitization" and "classical counter-conditioning". what this means is:
Letting the dog determine how close they are willing to go to the scary thing (the stairs) on thier own, and not pushing them further. Associate this distance with all kinds of good things - put the really good treats there, play games there, give belly rubs there. Repeated many times, the dog will come to feel more comfortable at that distance from the scary thing, and will be willing to go a bit closer. So this is the new threshold distance where you now bring out all the good stuff. And so on.
One way you could do this is to take his most favorite treats and dump them all over the floor at the foot of the stairs, and on the first step. And just leave them there and go about your business, or hang out close by. Sooner or later the dog will show an interest in the treats but be concerned about being near the stairs. Let the dog take his time getting at the treats, don't interfere. Depending on how afraid he is it may take days for him to get comfortable enough to actually eat any of them (you might want to replace or pick up the leftover treats at the end of the day!) But sooner or later, if he is not rushed, and the treats are really good, he will be willing to go nearer and then eventually go on the first step. And then on the second step and so on.
The key is to not rush things, don't coddle or soothe the dog, just act nonchalant about the whole thing and let him set the pace. There's no way to tell how much time this will take, each dog is different. Some dogs get over their fears in a few sessions, others take months. This is not to be discouraging, just realistic. But rushing things at any stage will put things back to square zero. So if you really need him to be upstairs before he is willing to climb it himself, I would continue to carry him for now, so as to not perpetuate his fear, and then separately work on desensitizing and conditioning him to accept going on the stairs by himselff at his own pace.
Also, are the stairs carpeted? I know many dogs are afraid of uncarpeted stairs because they are slippery and the dog feels unsure about their footing....My dog absolutely will not go up stairs that are open-ended or have holes in the steps (the kind where you can see through them to the ground below). I have not encountered these types of stairs in public places that I take my dog to, often enough to work with him on that issue, we just take the elevator instead! but closed stairs and carpeted stairs he has no problem with. good luck with this!!
How many stairs do you have? Do you have a spot in your house where you have 2 or 3 steps? How about the front porch of your house?
