Approximate bound-state solutions of the Dirac equation with q-deformed Woods-Saxon (WS) plus a new generalized ring-shaped (RS) potential are obtained for any arbitrary l-state. The energy eigenvalue equation and corresponding two-component wave functions are calculated by solving the radial and angular wave equations within a shortcut of the Nikiforov-Uvarov (NU) 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 RS Hulthen potential and the standard usual spherical WS potential (q = 1).