Exchange bias and coercivity of two dimensional (2-D) Co-Cr2O3 nanodots of different lateral sizes (120 nm and 240 nm) have been measured to investigate the effects of nanostructuring in exchange coupled systems. Triangular nanodots were prepared using polystyrene nanosphere lithography in conjunction with magnetron sputtering. The thickness of Co in the nanodots has been varied from 5 to 12 nm, while the thickness of Cr2O3 has been kept constant (23 nm) for all samples. Continuous films with the same thicknesses have also been investigated and compared with purely ferromagnetic (Co) and exchange biased (Co/Cr2O3) nanodots in order to study the effect of discretization on the magnetic properties. The coercivity of Co nanodots was found to be larger than that of both Co and Co/Cr2O3 continuous thin films. The Co/Cr2O3 nanodots showed a very large increase in exchange bias and coercivity over that of the continuous exchange biased films. The results have been used to estimate the effective interfacial coupling constant of the Co/Cr2O3 system, which is found to increase due to nanostructuring. These effects have been explained in terms of interfacial and configurational anisotropy of the nanostructures.