Monte Carlo simulations are performed in the Canonical ensemble to determine the equilibrium configurations of the counterions and co-ions in the vicinity of two charged hard disks at fixed separations. Derivation of the electrostatic energy and the ionic configurational entropy is used to determine the relative stability of two charged platelets as a function of their separation and relative orientation. An effective pair potential is derived from the free energy variation and may be used in the framework of the one component plasma to model suspensions of charged platelets. Finally, the variation of the free energy of two charged colloids in the presence of salt may be reproduced by Yukawa potential with a residual charge equal to 7% of the nominal electric charge of the colloids.