  We define deformation rings for potentially semi-stable deformations of fixed
discrete series inertial type in dimension $2$. In the case of representations
of the Galois group of $\mathbf{Q}_p$, we prove an analogue of the
Breuil-M\'ezard conjecture for these rings. As an application, we give some
results on the existence of congruences modulo $p$ for newforms in
$S_k(\Gamma_0(p))$.
