  Approximate bound state solutions of the Dirac equation with -deformed
Woods-Saxon plus a new generalized ring-shaped potential are obtained for any
arbitrary L-state. The energy eigenvalue equation and corresponding
two-component wave function are calculated by solving the radial and angular
wave equations within a shortcut of the Nikiforov-Uvarov method. The solutions
of the radial and polar angular parts of the wave function are expressed in
terms of the Jacobi polynomials. A new approximation being expressed in terms
of the potential parameters is carried out to deal with the strong singular
centrifugal potential term L(L+1)/r^2. Under some limitations, we can obtain
solution for the ring-shaped Hulth\'en potential and the standard usual
spherical Woods-Saxon potential (q=1).
