We present the sensitivity of the Parkes Pulsar Timing Array to gravitational waves (GWs) emitted by individual supermassive black hole binary systems in the early phases of coalescing at the cores of merged galaxies. Our analysis includes a detailed study of the effects of fitting a pulsar timing model to non-white timing residuals. Pulsar timing is sensitive at nanoHertz frequencies and hence complementary to Laser Interferometer Gravitational-Wave Observatory and Laser Interferometer Space Antenna. We place a sky-averaged constraint on the merger rate of nearby (z < 0.6) black hole binaries in the early phases of coalescence with a chirp mass of 1010 M☉ of less than one merger every 7 yr. The prospects for future GW astronomy of this type with the proposed Square Kilometre Array telescope are discussed.