  Pulsar timing observations are used to place constraints on the rate of
coalescence of supermassive black-hole (SMBH) binaries as a function of mass
and redshift. In contrast to the indirect constraints obtained from other
techniques, pulsar timing observations provide a direct constraint on the
black-hole merger rate. This is possible since pulsar timing is sensitive to
the gravitational waves (GWs) emitted by these sources in the final stages of
their evolution. We find that upper bounds calculated from the recently
published Parkes Pulsar Timing Array data are just above theoretical
predictions for redshifts below 10. In the future, with improved timing
precision and longer data spans, we show that a non-detection of GWs will rule
out some of the available parameter space in a particular class of SMBH binary
merger models. We also show that if we can time a set of pulsars to 10ns timing
accuracy, for example, using the proposed Square Kilometre Array, it should be
possible to detect one or more individual SMBH binary systems.
