  We calculate the cross section for diffractive photoproduction of
opposite-charge pseudoscalar meson pairs $M^+M^- = \pi^+ \pi^-$, $K^+ K^-$,
$D^+ D^-$ and $B^+ B^-$ in a broad range of center-of-mass energies relevant
for GlueX/Hall D, FOCUS, COMPASS and HERA experiments. In the case of
$\pi^+\pi^-$ production we find that the interference of the $\rho^0$ resonance
and the two-pion continuum leads to a considerable deformation of the shape of
$\rho^0$ in agreement with the data from the ZEUS collaboration. We also
discuss the spectral shape of the $\rho^0$ as a function of the momentum
transfer and the contribution of higher partial waves to the $\pi^+\pi^-$ mass
spectrum. We predict a sizeable energy-dependent forward-backward asymmetry in
the Gottfried-Jackson frame. For the heavy meson production we find that the
cross section for diffractive production increases much slower than the one for
open charm or bottom production. We discuss lower and upper limits for the
cross sections for diffractive production of $D^+ D^-$ and $B^+ B^-$ pairs,
which we find can be as large as 10% of the open flavor production.
