Inelastic neutron scattering was used to search for an influence of superconductivity on the phonons in optimally doped and in slightly overdoped Ba(Fe_{1_x}Co_x)₂As₂, x = 0.06 and x = 0.10. The study focused on phonons with energies close to the superconducting gap energy 2Δ because it is well known that such phonons will respond most strongly to the opening of the gap. We were able to obtain high quality data but nevertheless, we could not detect any influence of superconductivity on the phonons, neither on the linewidths nor on the frequencies. Our results imply that any coupling of low energy phonons to the electrons has to be very small, much smaller than observed in conventional superconductors with a high T_c. Our results are in line with the low coupling strength predicted by density functional theory for the investigated phonon branches.