We study the zero temperature non-equilibrium dynamics of a fermionic superfluid in the BCS limit and in the presence of a drive leading to a time-dependent chemical potential μ(t). We choose a periodic driving protocol characterized by a frequency ω and compute the fermion density, the wavefunction overlap, and the residual energy of the system at the end of N periods of the drive. We demonstrate that the BCS self-consistency condition is crucial in shaping the long time behaviour of the fermions subjected to the drive and provide an analytical understanding of the behaviour of the fermion density nkF (where kF is the Fermi momentum vector) after a drive period and for large ω. We also show that the momentum distribution of the excitations generated due to such a drive bears the signature of the pairing symmetry and can be used, for example, to distinguish between s- and d-wave superfluids. We propose experiments to test our theory. © 2013 IOP Publishing Ltd.