  Let F be an unramified extension of Qp. The first aim of this work is to
develop a purely local method to compute the potentially Barsotti-Tate
deformations rings with tame Galois type of irreducible two-dimensional
representations of the absolute Galois group of F. We then apply our method in
the particular case where F has degree 2 over Q_p and determine this way almost
all these deformations rings. In this particular case, we observe a close
relationship between the structure of these deformations rings and the geometry
of the associated Kisin variety. As a corollary and still assuming that F has
degree 2 over Q_p, we prove, except in two very particular cases, a conjecture
of Kisin which predicts that intrinsic Galois multiplicities are all equal to 0
or 1.
