We use an integral equation scheme to obtain self-consistently the effective interaction between colloids in salt-free charged colloidal suspensions. The colloid-counterion direct correlation function (DCF) is obtained for the fixed colloid-colloid pair structure by solving the corresponding hypernetted-chain equation (HNC). This DCF is then used to formulate an effective colloid-colloid pair potential for which the one-component reference hypernetted-chain equation is solved. Both processes are iterated until self-consistency is achieved. Counterion-counterion correlations are considered linear and uncoupled from the rest of the correlations. The method is based on a similar treatment utilized in liquid metals [Phys. Rev. B 61, 11400 (2000)] and provides equivalent results to those obtained using the standard multicomponent HNC equation for mixtures of charged hard spheres. The theory proves rather accurate when compared with molecular dynamic simulations of charged hard and soft spheres for colloidal charges of up to 300. We study in detail the existence of net attractions between colloids in certain cases (especially in the presence of divalent and trivalent counterions) and how this attraction may lead to phase instability. The problem of the lack of solution of the integral equation for more realistic cases (larger charges) is also discussed.