  Motivated by the recent theoretical materials design of superconducting $d^9$
nickelates for which the charge transfer from the NiO$_2$ to the block layer is
completely suppressed [M. Hirayama $\textit{et al.}$, Phys. Rev. B
$\textbf{101}$, 075107 (2020)], we perform a calculation based on the dynamical
vertex approximation and obtain the phase diagram of RbCa$_2$NiO$_3$ and
$A_2$NiO$_2$Br$_2$ where $A$ is a cation with a valence of 2.5+. We show that
the phase diagram of these nickelates exhibits the same essential features as
those found in cuprates. Namely, superconductivity appears upon hole-doping
into an antiferromagnetic Mott insulator, and the superconducting transition
temperature shows a dome-like shape. This demonstrates that the electron
correlations play an essential role in nickelate superconductors and we can
control them by changing block layers.
