We develop a linear theory for the scattering of equatorial waves of a fixed frequency ω by islands and continental margins of arbitrary geometry by use of the boundary integral equation (BIE) method of Vianna and Holvorcem (Part I of this work). All the solutions of the equatorial β-plane dispersion relations at frequency ω are treated explicitly through the extensive use of exact Green's functions, so that the approach is more general and more rigorous than previous attempts to solve equatorial scattering problems, many of which employ the low-frequency and long-wave approximations. The numerical solution of the HIE is obtained through application of the boundary element method. A numerical study of the scattering of Rossby waves with periods between 50 and 90 days from the equatorial Atlantic western boundary is presented. Some of the resulting interference patterns exhibit a sharp amplitude maximum, whose center lies between 3-9N, 35-47W. The position, width and intensity of this maximum all depend on wave period. We find evidences that this maximum arises from the superposition of zonally damped equatorial modes (evanescent waves) excited at the western boundary. The largest pressure amplitudes along the boundary are found in the southern hemisphere between the Equator and 5S. The phase propagation along the boundary is generally northwestward, except at a few positions where the phase is stationary. We discuss similarities and differences between the calculated responses and observations of intraseasonal oscillations in the tropical Atlantic Ocean.