  We report the observation of multiple phonon satellite features in ultra thin
superlattices of form $n$SrIrO$_3$/$m$SrTiO$_3$ using resonant inelastic x-ray
scattering. As the values of $n$ and $m$ vary the energy loss spectra show a
systematic evolution in the relative intensity of the phonon satellites. Using
a closed-form solution for the cross section, we extract the variation in the
electron-phonon coupling strength as a function of $n$ and $m$. Combined with
the negligible carrier doping into the SrTiO$_3$ layers, these results indicate
that tuning of the electron-phonon coupling can be effectively decoupled from
doping. This work showcases both a feasible method to extract the
electron-phonon coupling in superlattices and unveils a potential route for
tuning this coupling which is often associated with superconductivity in
SrTiO$_3$-based systems.
