It is shown that the Fredholm method for the solution of integral equations can be adapted to solve the covariant scattering equations for the proton-neutron system and the meson-nucleon system. A practical method is devised for obtaining the binding energies of the deuteron and hyperon in a fully covariant way. As a test of the method it has been applied to the corresponding non-covariant equation for the deuteron, and satisfactory numerical results are obtained.