  We explore the properties of dense star clusters that are likely to be the
nurseries of stellar black holes pairing in close binaries. We combine a
cosmological model of globular cluster formation with analytic prescriptions
for the dynamical assembly and evolution of black hole binaries to constrain
which types of clusters are most likely to form binaries tight enough to
coalesce within a Hubble time. We find that black hole binaries which are
ejected and later merge ex-situ form in clusters of a characteristic mass
$M_{\rm cl} \sim 10^{5.3}M_{\odot}$, whereas binaries which merge in-situ form
in more massive clusters, $M_{\rm cl} \sim 10^{5.7}M_{\odot}$. The clusters
which dominate the production of black hole binaries are similar in age and
metallicity to the entire population. Finally, we estimate an approximate
cosmic black hole merger rate of dynamically assembled binaries using the mean
black hole mass for each cluster given its metallicity. We find an intrinsic
rate of $\sim 6\,\mathrm{Gpc\,yr^{-1}}$ at $z=0$, a weakly increasing merger
rate out to $z=1.5$, and then a decrease out to $z=4$. Our results can be used
to provide a cosmological context and choose initial conditions in numerical
studies of black hole binaries assembled in star clusters.
