This is certainly something that I have experience of. As you will perhaps read from
my own dog's blog, my dog Ellie was a litter runt, and this means that she is a naturally very timid dog. Very timid indeed.
If I take my own dog as an example, I couldn't train heel-work for some time, because my height scared her. She wouldn't come near me without cowering.
You are right, having a timid dog does bring about some really quite unique training challenges. Last weekend, my dog passed her Gold level Kennel Club Good Citizen exam, and she's still growing in confidence each day, so you can turn a timid dog around to some extent For what it's worth, here's my advice:
Allow the dog to take some liberties. This means letting her jump on the couch, and maybe sleeping on your bed. The timid dog needs to learn to have ultimate trust in you, and she will gain comfort from being close to you. If you push her away, then she feels that she has nobody to run to when she needs to. You can stop this when she develops more confidence, as I have just done with my own dog. (She's no longer allowed on the furniture, after having been allowed on it for the past year.)
When the dog gets it right, make her feel like a million dollars. Over-praise if you have to. Conversely, when she gets it wrong, do nothing. A timid dog needs no punishment, or even harsh words. It can only serve to set them back and make them more timid.
Work at the dog's level. This was how I finally got around the height issue with my own dog. I had to train her with me sitting or kneeling on the floor so that I wasn't towering over her. I can't over-state the difference this small move made.
Play tug, and let her win a few times. Then even allow her to run away with the toy with you pretending to chase her. Ellie now loves this.
Give her plenty of opportunities each day to succeed and to feel special. Each success she achieves will build her confidence. Spend a few minutes each day on the floor, training with her, even if it's behaviours that she already knows. It's all about building her confidence.
Never ask for more than she can deliver. If she has to cower, then you've asked for too much. Just remember next time, and lower the expectations.
Try doing some exercises which give her physical confidence. I, for example, used to take the cushions from my sofa and balance them on top of each other, and encourage Ellie to jump on top, gradually increasing the height each time. I would always make sure that she never feel, but would allow the cushions to sway around when she was on them. Again, it's about the confidence.
At two years, your own dog is still plenty young enough to gain in confidence. Hope it helps.