We study the dynamical correlation functions of the Richardson pairing model (also known as the reduced- or discrete-state Bardeen, Cooper, Schrieffer model) in the canonical ensemble. We use the algebraic Bethe Ansatz formalism, which gives exact expressions for the form factors of the most important observables. By summing these form factors over a relevant set of states, we obtain very precise estimates of the correlation functions, as confirmed by global sum rules (saturation above 99% in all cases considered). Unlike the case of many other Bethe Ansatz solvable theories, simple two-particle states are sufficient to achieve such saturations, even in the thermodynamic limit. We provide explicit results at half filling and discuss their finite-size scaling behavior.