  We search for candidate island regions in FRW cosmologies supported by
radiation, cosmological constant $\Lambda$, and non-zero spatial curvature. The
radiation is assumed to be in a thermal state. We apply the necessary
conditions introduced in [arXiv:2008.01022]. Both for the open and closed
universes with $\Lambda<0$, the Friedmann equation admits recollapsing
solutions with a time-symmetric slice. In the case of closed universes, there
is always an island that is the whole Cauchy slice. However, for $\Lambda<0$,
we also find another finite-sized candidate island region, in the middle of the
spacetime, at the turnaround time. In the case of the open universes, we only
find a candidate island region for $\Lambda<0$, that appears at the turnaround
time. It starts from a finite value of the radial coordinate and extends to
infinity. Looking at both open and closed universes, we conclude that the key
ingredient that allows the existence of islands is the negative cosmological
constant. We provide analytic results along the time-symmetric slices and
support our results with numerics in the whole spacetime.
