  We present a study of the central exclusive production of light meson pairs,
concentrating on the region of lower invariant masses of the central system
and/or meson transverse momentum, where perturbative QCD cannot be reliably
applied. We describe in detail a phenomenological model, using the tools of
Regge theory, that may be applied with some success in this regime, and we
present the new, publicly available, Dime Monte Carlo (MC) implementation of
this for $\pi\pi$, $KK$ and $\rho\rho$ production. The MC includes a fully
differential treatment of the survival factor, which in general depends on all
kinematic variables, as well as allowing for the so far reasonably
unconstrained model parameters to be set by the user. We present predictions
for the Tevatron and LHC and show how future measurements may further test this
Regge--based approach, as well as the soft hadronic model required to calculate
the survival factor, in particular in the presence of tagged protons.
