  We continue our analysis of Ising models on the (directed) Erd\H{o}s-R\'enyi
random graph $G(N,p)$. We prove a quenched Central Limit Theorem for the
magnetization and describe the fluctuations of the log-partition function. In
the current note we consider the low temperature regime $\beta>1$ and the case
when an external magnetic field is present. In both cases, we assume that
$p=p(N)$ satisfies $p^3N \to \infty$.
