  In this paper we consider the Klein-Gordon equation on spherically symmetric
background spacetimes with a constant area radius. The spacetimes under
consideration are Nariai and Pleba\'nski-Hacyan, and can be considered constant
radius limits of Reissner-Nordstr\"om-de Sitter spacetimes. We prove
boundedness in the case of a non-negative Klein Gordon mass and decay unless
the mass is zero. In the latter case we prove decay of solutions that are
supported on all harmonic modes with angular momentum l greater or equal to 1.
We show that the l=0 modes of solutions to the massless Klein-Gordon equation
do not decay. They are subject to conservation laws along degenerate Killing
horizons. We apply the estimates in Nariai to give decay of solutions to the
massive Klein-Gordon equation on an n-dimensional de Sitter background, using
only the vector field method and with no restrictions on the positive
Klein-Gordon mass.
