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-neighbor 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 nonzero d-wave as well as extended s-wave pairing amplitude for Delta similar to U » 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 solved using continuous time quantum Monte Carlo. 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.