  It is shown by Monte Carlo method that the finite size scaling (FSS) holds in
the two dimensional random-coupled Ising ferromagnet. It is also demonstrated
that the form of universal FSS function constructed via novel FSS scheme
depends on the strength of the random coupling for strongly disordered cases.
Monte Carlo measurements of thermodynamic (infinite volume limit) data of the
correlation length ($\xi$) up to $\xi \simeq 200$ along with measurements of
the fourth order cumulant ratio (Binder's ratio) at criticality are reported
and analyzed in view of two competing scenarios. It is demonstrated that the
data are almost exclusively consistent with the scenario of weak universality.
