  The recently discovered high-T$_C$ superconductor La$_3$Ni$_2$O$_7$ has
sparked renewed interest in the unconventional superconductivity. Here we study
superconductivity in pressurized La$_3$Ni$_2$O$_7$ based on a bilayer
two-orbital $t-J$ model, using the renormalized mean-field theory. Our results
reveal a robust $s^\pm-$wave pairing driven by the inter-layer $d_{z^2}$
magnetic coupling, which exhibits a transition temperature within the same
order of magnitude as the experimentally observed $T_c \sim 80$ K. We establish
a comprehensive superconducting phase diagram in the doping plane. Notably, the
La$_3$Ni$_2$O$_7$ under pressure is found situated roughly in the optimal
doping regime of the phase diagram. When the $d_{x^2-y^2}$ orbital becomes
close to half-filling, $d-$wave and $d+is$ pairing can emerge from the system.
We discuss the interplay between Fermi surface topology and different pairing
symmetries. The stability of the $s^\pm-$wave pairing against Hund's coupling
and other magnetic exchange couplings is discussed.
