  We give an expansion of the solution of the evolution equation for the
massless Dirac fields in the outer region of de Sitter-Reissner-Nordstr\"om
black hole in terms of resonances. By means of this method we describe the
decay of local energy for compactly supported data. The proof uses the cut-off
resolvent estimates for the semi-classical Schr\"odinger operators from Bony
and H\"afner, 2008. The method extends to the Dirac operators on spherically
symmetric asymptotically hyperbolic manifolds.
