We study a strongly correlated fermionic model with attractive interactions in the presence of disorder in two spatial dimensions. Our model has been designed so that it can be solved using the recently discovered meron-cluster approach. Although the model is unconventional it has the same symmetries of the Hubbard model. Since the naive algorithm is inefficient, we develop a new algorithm by combining the meron-cluster technique with the directed-loop update. This combination allows us to

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... te the pair susceptibility and the winding number susceptibility accurately. We find that the s-wave superconductivity, present in the clean model, does not disappear until the disorder reaches a temperature dependent critical strength. The critical behavior as a function of disorder close to the phase transition belongs to the Berezinsky-Kosterlitz-Thouless universality class as expected. The fermionic degrees of freedom, although present, do not appear to play an important role near the phase transition.