The mean field vortex phase diagram of a quasi-two-dimensional superconductor with a nodal d-wave pairing and with strong Pauli spin depairing is studied in the parallel field case in order to examine the effect of gap nodes on the stability of a Fulde-Ferrell-Larkin-Ovchinnikov- (FFLO-) like vortex lattice. We find through a heuristic argument and a model calculation with a fourfold anisotropic Fermi surface that the FFLO-like state is relatively suppressed as the field approaches a nodal direction. When taking account of available experimental results together, the present result strongly suggests that the pairing symmetry of CeCoIn5 should be of dxy type.