  We show by extensive numerical simulations and analytical variational
calculations that elongated binary non-miscible Bose-Einstein condensates
subject to periodic modulations of the radial confinement exhibit a Faraday
instability similar to that seen in one-component condensates. Considering the
hyperfine states of $^{87}$Rb condensates, we show that there are two
experimentally relevant stationary state configurations: the one in which the
components form a dark-bright symbiotic pair (the ground state of the system),
and the one in which the components are segregated (first excited state). For
each of these two configurations, we show numerically that far from resonances
the Faraday waves excited in the two components are of similar periods, emerge
simultaneously, and do not impact the dynamics of the bulk of the condensate.
We derive analytically the period of the Faraday waves using a variational
treatment of the coupled Gross-Pitaevskii equations combined with a
Mathieu-type analysis for the selection mechanism of the excited waves.
Finally, we show that for a modulation frequency close to twice that of the
radial trapping, the emergent surface waves fade out in favor of a forceful
collective mode that turns the two condensate components miscible.
