  There are certain black hole solutions in general relativity (GR) which are
conformally related to the stationary solutions in GR. It is not obvious that
the horizon entropy of these spacetimes is also one quarter of the area of
horizon, like the stationary ones. Here I study this topic in the context of
Virasoro algebra and Cardy formula. Using the fact that the conformal spacetime
admits conformal Killing vector and the horizon is determined by the vanishing
of the norm of it, the diffemorphisms are obtained which keep the near horizon
structure invariant. The Noether charge and a bracket among them corresponding
to these vectors are calculated in this region. Finally, they are evaluated for
the Sultana-Dyer (SD) black hole, which is conformal to the Schwarzschild
metric. It is found that the bracket is identical to the usual Virasoro algebra
with the central extension. Identifying the zero mode eigenvalue and the
central charge, the entropy of the SD horizon is obtained by using Cardy
formula. Interestingly, this is again one quarter of the horizon area. Only
difference in this case is that the area is modified by the conformal factor
compared to that of the stationary one. The analysis gives a direct proof of
the earlier assumption.
