  We examine the effect of the intra- and interspecies scattering lengths on
the dynamics of a two-component Bose-Einstein condensate, particularly focusing
on the existence and stability of solitonic excitations. For each type of
possible soliton pairs stability ranges are presented in tabulated form. We
also compare the numerically established stability of bright-bright,
bright-dark and dark-dark solitons with our analytical prediction and with that
of Painlev\'e-analysis of the dynamical equation. We demonstrate that tuning
the inter-species scattering length away from the predicted value (keeping the
intra-species coupling fixed) breaks the stability of the soliton pairs.
