We analytically study the background stability of dark strongly localized vectorial modes in discrete cubic media with self- and cross-phase modulation. The instability regions are identified as a function of the linear and non-linear coupling strength as well as the ratio between the background amplitudes of the two components. The respective instability gain is calculated. Approximate analytical solutions for vectorial discrete solitons of different topologies are derived. The analytical results obtained are confirmed by direct numerical simulations.