  Experimental evidence suggests that the Fulde-Ferrell-Larkin-Ovchinnikov
(FFLO) state may be realized in the unconventional, heavy-fermion
superconductor CeCoIn$_5$. We present a self-consistent calculation of the
field versus temperature phase diagram and order parameter structures for the
FFLO states of quasi-two-dimensional d-wave superconductors. We calculate the
spatially nonuniform order parameter, free energy density, and local density of
states for magnetic fields parallel to the superconducting planes. We predict
that the lower critical magnetic field transition between the spatially uniform
and nonuniform FFLO state is second order. We discuss the signatures of the
nonuniform FFLO state which should be observable in scanning tunneling
microscopy measurements of the local density of states.
