I used to have a rabbit that would always bite if I held her. Other than that, she was very friendly towards me and enjoyed my company and loved being pet (wasn't too friendly with strangers though. Unfortunate but funny story, there was a really annoying girl over at my house and I told her not to touch the rabbits. Of course she didn't listen and ended up with a bloody finger). Besides strangers, my rabbit was very friendly besides the part where I had to pick her up. So since nothing worked, I would simply grab the skin on her back (you grab a very thick section of skin otherwise it can be painful. You could probably youtube or google to see how it looks) and gently lift her while supporting her bottom and holding her as close to me as possible. Some people say this hurts them, but from my experience with many rabbits, I did not see them experiencing any pain. Grabbing by the ears is DEFINITELY a no-no, but I've always seen that they are fine with the skin on their back.
However, if you stop petting your rabbit on the back and only pick them up that way, they will stop liking being touched on their back. But if you keep petting them regularly they should be fine. So just keep that in mind.
I once adopted an adult rabbit and it was very obvious to me that her previous owners never touched her besides to pick her up that way, but she was still very friendly. Whenever I'd try to pet her she would literally slinky away from me from under my hand. She wasn't fearful, but uncomfortable.
Oh and also, you must be very gentle but firm when picking them up this way because they can kick. I once had one rabbit break off an entire nail this way, and I've been scratched too. But experience helps and I never have problems anymore.
Some people will disagree with me, and if you are uncomfortable picking them up this way, definitely disregard my advice and don't do it. This is my two cents and if people disagree with me, I am totally okay with that. But for me this is the only thing that works with difficult rabbits. If youre not confident this way, it is safer not to do it because you can end up doing more harm than good.
Another idea though, you could try to make some sort of little rugs and put them on the stairs for your rabbit to be able to walk on without slipping or anything, and them remove them when it isnt needed. Just an idea