  We perform a search for gravitational waves (GWs) from several supermassive
binary black hole (SMBBH) candidates (NGC 5548, Mrk 231, OJ 287, PG 1302-102,
NGC 4151, Ark 120 and 3C 66B) in long-term timing observations of the pulsar
PSR J1909$-$3744 obtained using the Parkes radio telescope. No statistically
significant signals were found. We constrain the chirp masses of those SMBBH
candidates and find the chirp mass of NGC 5548 and 3C 66B to be less than $2.4
\times 10^9\,\rm M_{\odot}$ and $2.5 \times 10^9\,\rm M_{\odot}$ (with 95%
confidence), respectively. Our upper limits remain a factor of 3 to 370 above
the likely chirp masses for these candidates as estimated from other
approaches. The observations processed here provide upper limits on the GW
strain amplitude that improve upon the results from the first Parkes Pulsar
Timing Array data release by a factor of 2 to 7. We investigate how information
about the orbital parameters can help improve the search sensitivity for
individual SMBBH systems. Finally, we show that these limits are insensitive to
uncertainties in the Solar System ephemeris model.
