  We present a simple way of constructing conformal couplings of a scalar field
to higher order Euler densities. This is done by constructing a four-rank
tensor involving the curvature and derivatives of the field, which transforms
covariantly under local Weyl rescalings. The equation of motion for the field,
as well as its energy momentum tensor are shown to be of second order. The
field equations for the spherically symmetric ansatz are integrated, and for
generic non-homogeneous couplings, the solution is given in terms of a
polynomial equation, in close analogy with Lovelock theories.
