  In the present work, we generalize earlier considerations for intrinsic
localized modes consisting of a few excited sites, as developed in the
one-component discrete nonlinear Schrodinger equation model, to the case of
two-component systems. We consider all the different combinations of "up" (zero
phase) and "down" ({\pi} phase) site excitations and are able to compute not
only the corresponding existence curves, but also the eigenvalue dependences of
the small eigenvalues potentially responsible for instabilities, as a function
of the nonlinear parameters of the model representing the self/cross phase
modulation in optics and the scattering length ratios in the case of matter
waves in optical lattices. We corroborate these analytical predictions by means
of direct numerical computations. We infer that all the modes which bear two
adjacent nodes with the same phase are unstable in the two component case and
the only solutions that may be linear stable are ones where each set of
adjacent nodes, in each component is out of phase.
