  We study ultracold fermionic atoms trapped in an optical lattice with
harmonic confinement by means of the dynamical mean-field approximation. It is
demonstrated that a supersolid state, where an s-wave superfluid coexists with
a density-wave state with a checkerboard pattern, is stabilized by attractive
onsite interactions on a square lattice. Our new finding here is that a
confining potential plays an invaluable role in stabilizing the supersolid
state. We establish a rich phase diagram at low temperatures, which clearly
shows how the insulator, the density wave and the superfluid compete with each
other to produce an intriguing domain structure. Our results shed light on the
possibility of the supersolid state in fermionic optical lattice systems.
