We report measurements of the specific heat and electrical resistivity of Ca₃(Ir_0.91Co_0.09)₄Sn₁₃ in comparison to Ca₃Ir₄Sn₁₃. The Co substitution was chosen to suppress the structural anomaly T^∗ = 38 K reported in Ca₃Ir₄Sn₁₃. While the superconducting transition temperature of Ca₃(Ir_0.91Co_0.09)₄Sn₁₃ is slightly higher than in the stoichiometric parent compound Ca₃Ir₄Sn₁₃, and it displays a stronger superconducting coupling strength, the absence of a structural phase transition allows us to determine the spectral distribution of phonon states and its relation to superconductivity. The phonon density of states F(ω) and the spectral electron-phonon scattering function α_tr²F(ω) are determined by deconvolution of the specific heat and electrical resistivity, respectively. A dominant mode appears in both histograms at ħω = 12 meV, which indicates that this phonon mode is responsible for the superconductivity in Ca₃(Ir_0.91Co_0.09)₄Sn₁₃. The data suggest that superconductivity in this material class can be conclusively explained within a conventional strong -coupling phonon-mediated scenario.