  Recently, high temperature ($T_c\approx 80$K) superconductivity (SC) has been
discovered in La$_3$Ni$_2$O$_7$ (LNO) under pressure. Question arises whether
the transition temperature $T_c$ could be further enhanced under suitable
conditions. A possible route for realizing higher $T_c$ is element
substitution. Similar SC could appear in rare-earth (RE) R$_3$Ni$_2$O$_7$ (RNO,
R=RE element) material series under pressure. The electronic properties in the
RNO materials are dominated by the Ni $3d$ orbitals in the bilayer NiO$_2$
plane. In the strong coupling limit, the SC could be fully characterized by a
bilayer single $3d_{x^2-y^2}$-orbital $t$-$J_{\parallel}$-$J_{\perp}$ model.
Under RE element substitution from La to RE element, the lattice constant
decreases and the electronic hopping increases, leading to stronger
superexchanges between the $3d_{x^2-y^2}$ orbitals. Based on the slave-boson
mean-field theory, we explore the pairing nature and the evolution of $T_c$ in
RNO materials. Consequently, it is found that the element substitution does not
alter the pairing nature, i.e. the inter-layer $s$-wave pairing is always
favored in RNO. However, the $T_c$ increases from La to Sm and a nearly doubled
$T_c$ is achieved for SmNO. This work provides evidence for possible higher
$T_c$ R$_3$Ni$_2$O$_7$ materials, which may be realized in further experiments.
