Many things in our best models of physics are discrete, but as far as I know, our coordinates (time, space, or four-dimensional space-time coordinates) are never discrete. Even something like quantum field theory, which treats things in a non-intuitively discrete way does not do this. For example, we might view the process of an electron scattering off another electron as an exchange of many discrete photons between the two electrons, but it is all written in terms of integrals or derivatives, rather than differences or sums.