  We construct a class of coherent spin-network states that capture proprieties
of curved space-times of the Friedmann-Lama\^itre-Robertson-Walker type on
which they are peaked. The data coded by a coherent state are associated to a
cellular decomposition of a spatial ($t=$const.) section with dual graph given
by the complete five-vertex graph, though the construction can be easily
generalized to other graphs. The labels of coherent states are complex $SL(2,
\mathbbm{C})$ variables, one for each link of the graph and are computed
through a smearing process starting from a continuum extrinsic and intrinsic
geometry of the canonical surface. The construction covers both Euclidean and
Lorentzian signatures; in the Euclidean case and in the limit of flat space we
reproduce the simplicial 4-simplex semiclassical states used in Spin Foams.
