  We develop the formalism for coherent two pion photoproduction in nuclei and
perform actual calculations of cross sections for $\pi^-\pi^+$ and $\pi^0\pi^0$
photoproduction on $^{12}C$. We find that due to the isospin symmetry the cross
section for $\pi^0\pi^0$ production is very small and has a maximum when the
pions propagate together. However, the kinematical region where the energies
and polar angles of the two $\pi^0$ mesons are equal and their relative
azimuthal angle $\phi=180^0$ is forbidden. Conversely in the $\pi^-\pi^+$
production the pions prefer to have a relative azimuthal angle 180$^0$ and the
production of the pions propagating together is suppressed. The dominant
one-body mechanism in both channels is related to the excitation of the
$\Delta$ isobar. Hence the reaction can serve as a source of information about
$\Delta$'s properties in nucleus. We have found that the reaction is sensitive
to effects of the pion and $\Delta$ renormalization in the nuclear medium,
similar to those found in the coherent $(\gamma,\pi^0)$ reaction, but magnified
because of the presence of the two pions.
