  We identify an anisotropic divergence-free conformal Killing tensor $K_{jl}$
for static spherically symmetric spacetimes, and write the conformal Killing
gravity equations as Einstein equations augmented by this tensor. The field
equations are of second order: this fact allows for analytic solutions and
considerably simplifies the derivation of results of previous studies based on
the original Harada equations. In particular, we prove the equivalence of the
known third order field equations, with the second order ones obtained by us in
the conformal Killing parametrization. The structure of the Ricci tensor and of
the conformal Killing tensor are compatible with both anisotropic fluid sources
and (non)-linear electrodynamics. We reobtain covariantly and in simple steps
the general static spherical solutions for vacuum and linear electrodynamics.
Moreover we recover the purely magnetic Lagrangian functions that induce
metrics of interest for black holes.
