Oppositely charged bipolar colloids or colloids decorated with complementary deoxyribonucleic acid (DNA) on their surfaces are special kinds of patchy particles where only patch and non-patch parts are attractive. These are classified as inverse patchy colloids (IPCs). In this work, equilibrium self-assembly of IPC in two-dimensions is reported using Monte Carlo simulations. Square (SCs) and triangular crystals (TCs) are found to be stable at 0.5 patch coverage. Upon decreasing the patch coverage to 0.33, the regular SC is destabilized; instead rhombic and TCs are found to be stable. At low patch coverages such as 0.22 and 0.12, only TC is stabilized at high density. Particles of all the patch coverages show kinetically stable cluster phases of different shapes and sizes at low densities, and the average cluster size depends on the patch coverage and particle density. State-diagrams showing all the stable phases for each patch coverage are presented. Ordered phases are characterized by bond order parameters ψ 4, ψ 6 and radial distribution function. The effect of polydispersity in patch coverage on the polarization of the stable structures are also studied. The study demonstrates that IPCs can stabilize various ordered two-dimensional structures by tuning the size of the patch, density and interaction strengths. © 2021 IOP Publishing Ltd.