  We investigate the ionic Hubbard model (IHM) at half-filling in the limit of
strong correlations and large ionic potential. The low energy effective
Hamiltonian in this limit, obtained by a similarity transformation, is a
modified $t-J$ model with effective second neighbour hopping terms. We explore
the possibilities of d-wave pairing and extended s-wave pairing superconducting
(SC) phases on a two dimensional square lattice at zero temperature within a
Gutzwiller projected renormalized mean field theory. In the sector of solutions
that forbid spin ordering, the system shows a finite non-zero d-wave as well as
extended s-wave pairing amplitude for $\Delta \sim U \gg t$. The width of the
superconducting phase in $U-\Delta$ regime shrinks with increase in $U$ and
$\Delta$, though the extended s-wave pairing phase is higher in energy than the
d-wave pairing superconducting phase. But in a spin resolved renormalized mean
field calculation, which allows for an antiferromagnetic (AF) order along with
the d-wave or extended s-wave pairing, the SC phase is no longer viable and the
system shows a direct transition from an AF ordered phase to a paramagnetic
band insulator. Except for a thin sliver of a half-metallic AF phase close to
the AF transition point, most of the AF ordered phase is a Mott insulator. We
benchmarked the AF Mott insulator to band insulator transition within the
Gutzwiller projected renormalized mean field theory against the dynamical mean
field theory (DMFT) solved using continuous time quantum Monte-Carlo (CTQMC).
Our work suggests that the ground state phase diagram of the IHM at
half-filling in the limit of extreme correlations does not have any SC phase.
The SC phase seen in the paramagnetic sector is a metastable phase, being
higher in energy than the AF Mott insulator phase.
