We investigate the non-equilibrium behavior of BCS superconductors subjected to slow ramps of their internal interaction strength. We identify three dynamical regimes as a function of ramp duration. For short ramp times, these systems become non-superconducting; however, fermions with opposite momenta remain paired albeit with reduced amplitudes, and the associated pair amplitude distribution is non-thermal. In this first regime, the disappearance of superconductivity is due to the loss of phase coherence between pairs. By contrast, for intermediate ramp times, superconductivity survives but the magnitude of the order parameter is reduced and presents long-lived oscillations. Finally, for long ramp times, phase coherence is almost fully retained during the slow interaction quench, and the steady-state is characterized by a thermal-like pair amplitude distribution. Using this approach, one can therefore dynamically tune the coherence between pairs in order to control the magnitude of the superconducting order parameter and even engineer a non-equilibrium state made of pre-formed pairs.