Thanks, I succeeded in exporting it, but now I have another problem. I have the newest version of Blender and NIF scripts (2.44 Blender and 2.0.5 NIF scripts, I think). Now my cuirass looks alright in NifSkope but it's invisible in game. I thought it was a problem of the Scene Root in NifSkope, but I checked and it was already #0. And since I did what you said (imported only the armor and didn't parent anything) it can't depend from the skeleton.
Sorry, I know I'm hopeless..