  White dwarf spectroscopy shows that nearly half of white dwarf atmospheres
contain metals that must have been accreted from planetary material that
survived the red giant phases of stellar evolution. We can use metal pollution
in white dwarf atmospheres as flags, signalling recent accretion, in order to
prioritize an efficient sample of white dwarfs to search for transiting
material. We present a search for planetesimals orbiting six nearby white
dwarfs with the CHEOPS spacecraft. The targets are relatively faint for CHEOPS,
$11$ mag $< G < 12.8$ mag. We use aperture photometry data products from the
CHEOPS mission as well as custom PSF photometry to search for periodic
variations in flux due to transiting planetesimals. We detect no significant
variations in flux that cannot be attributed to spacecraft systematics, despite
reaching a photometric precision of $<2$ ppt in 60 s exposures on each target.
We simulate observations to show that the small survey is sensitive primarily
to Moon-sized transiting objects with periods $3$ hr $< P < 10$ hr, with radii
$R \gtrsim 1000$ km.
