  In this note, we prove two Kazdan-Warner type identities involving
$v^{(2k)}$, the renormalized volume coefficients of a Riemannian manifold
$(M^n,g)$, and $G_{2r}$, the so-called Gauss-Bonnet curvature, and a conformal
Killing vector field on $(M^n,g)$. In the case when the Riemannian manifold is
locally conformally flat, $v^{(2k)}=(-2)^{-k}\sigma_k$,
$G_{2r}(g)=\frac{4^r(n-r)!r!}{(n-2r)!}\sigma_r$, and our results reduce to
earlier ones established by Viaclovsky and by the second author.
