My 10 month old girl is doing something very similar. It's not that she wants to nurse, it's that she is attempting to use my breast as a pacifier. What I did last week was I gave her some water from a cup instead. It made her stop crying, satisfied any thirst and she went back to sleep on her own.Prior to giving her the water she cried for about 15 minutes and absokutely refused to lay down on the bed or my shoulder.
Now, dont get me wrong, she still wakes wanting to nurse, but if I consistently were to give her water instead, I think it would stop in short time.
Also, I've noticed, when she sleeps with her dad, or when I'm not there, she doesnt do it. When she awakes and i'm not there, he says, "lay down and comforts her" and she goes back to sleep.
I hope this helps.