This is not the original reference, but the most general (i.e., applicable to the non-compact and pseudo-Riemannian cases) result I know is:

[Kühnel, W., & Rademacher, H.  Conformal diffeomorphisms preserving the Ricci tensor. Proceedings of the American Mathematical Society, 123 (1995), no. 9, 2841–2848.](http://www.ams.org/mathscinet-getitem?mr=1260173)

(The [article](http://www.ams.org/journals/proc/1995-123-09/S0002-9939-1995-1260173-6/home.html) is publicly available for free.)

Theorem 1* in there gives uniqueness in any case other than simply-connected, constant curvature spaces, and certain warped products with Ricci-flat spaces.

Check out the references in that paper, too.