  Observations of neutron star mergers in the late Universe have given
significant restrictions to the class of viable scalar-tensor theories. In this
paper we construct black holes within the "self-tuning" class of this
restricted set, whereby the bare cosmological constant is absorbed by the
dynamics of the scalar, giving a lower effective cosmological constant. We use
analytic expansions at the singularity, black hole and cosmological horizon,
and asymptotic region, coupled with numerical solutions, to find well-behaved
black holes that asymptote to the self-tuned de Sitter geometry. The geometry
differs from standard general relativity black holes near the horizon, and the
scalar field velocity provides a hair for the black holes.
