  In a previous paper, the authors showed that metrics which are asymptotic to
Anti-de Sitter-Schwarzschild metrics with positive mass admit a unique
foliation by stable spheres with constant mean curvature. In this paper we
extend that result to all asymptotically hyperbolic metrics for which the trace
of the mass term is positive. We do this by combining the Kazdan-Warner
obstructions with a theorem due to De Lellis and M\"uller.
