  We present a generalisation of the charged C-metric conformally coupled with
a scalar field in the presence of a cosmological constant. The solution is
asymptotically flat or a constant curvature spacetime. The spacetime metric has
the geometry of a usual charged C-metric with cosmological constant, where the
mass and charge are equal. When the cosmological constant is absent it is found
that the scalar field only blows up at the angular pole of the event horizon.
The presence of the cosmological constant can generically render the scalar
field regular where the metric is regular, pushing the singularity beyond the
event horizon. For certain cases of enhanced acceleration with a negative
cosmological constant, the conical singularity disappears all together and the
scalar field is everywhere regular. The black hole is then rather a black
string with its event horizon extending all the way to asymptotic infinity and
providing itself the necessary acceleration.
