  Emergence of superconductivity in a two-band system coupled with breathing
and Jahn-Teller phonons is discussed in a weak-coupling limit. With the use of
a standard quantum mechanical procedure, the phonon-mediated attraction is
derived. From the analysis of the model including such attraction, a BCS-like
formula for a superconducting transition temperature $T_{\rm c}$ is obtained.
When only the breathing phonon is considered, $T_{\rm c}$ is the same as that
of the one-band model. On the other hand, when Jahn-Teller phonons are active,
$T_{\rm c}$ is significantly enhanced by the interband attraction even within
the weak-coupling limit. Relevance of the present result to actual materials
such as iron pnictides is briefly commented.
