  Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably
related, we give an explicit construction of a Poincar\'e-Einstein
(pseudo-)metric with conformal infinity the conformal class of the product of
the initial metrics. We show that these metrics are equivalent to ambient
metrics for the given conformal structure. The ambient metrics have holonomy
that agrees with the conformal holonomy. In the generic case the ambient metric
arises directly as a product of the metric cones over the original Einstein
spaces. In general the conformal infinity of the Poincare metrics we construct
is not Einstein, and so this describes a class of non-conformally Einstein
metrics for which the (Fefferman-Graham) obstruction tensor vanishes.
