The coherent interactions between one-dimensional discrete spatial optical solitons, derived by Petviashvili iteration method, are numerically investigated with the split-step beam propagation method in light-induced planar waveguide arrays. The influences of the initial phase difference, the soliton peak intensities, the periods and intensities of the writing beams for waveguide arrays, and the amplitudes of the externally bias fields on the interactions between two discrete solitons are analyzed in detail. It is found that the interactions between two parallel discrete solitons with different initial phase differences behave in a way similar to that encountered in continuous media, i.e., in-phase (out-of-phase) discrete solitons attract (repel) each other, and the intermediates are always accompanied with energy transfer. In addition, the interaction processes are influenced by the variations of soliton peak intensities, the configurations of the light-induced waveguide arrays, and the amplitudes of the external bias fields.