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A stability method is used to assess possible values of interspecies scattering lengths a12 in two-component Bose-Einstein condensates described within the Gross-Pitaevskii approximation. The technique, based on a recent stability analysis of solitonic excitations in two-component Bose-Einstein condensates, is applied to ninety combinations of atomic alkali pairs with given singlet and triplet intraspecies scattering lengths as input parameters. Results obtained for values of a12 are in a reasonable agreement with the few ones available in the literature and with those obtained from a Painleve analysis of the coupled Gross-Pitaevskii equations.