In this paper we present Green function technique applied to calculations of spin-spin correlations in systems governed by Ising Hamiltonian. This offers approximate yet reasonably accurate analytical results, as an alternative approach to direct computer simulation. Local spin operators are represented in terms of particle operators for fermions. Chain of Green functions for local magnetization on given site involves nearest neighbors and it is decoupled at the next-nearest-neighbors level. Therefore, still accounts at the lowest level for magnetic correlations between nearest neighbors. This technique was applied to binary alloy A x B 1-x with given atomic short range order. Calculations for stoichiometric x=1/2 composition show how temperature dependence of magnetization and spin-spin correlations are modified when atomic order parameter changes. We scanned this parameter from the case of ordered binary alloy, via random alloy, to clusterlike structure. In model calculations we (a) confirm characteristic λ -like shape of the magnetic specific heat near Curie temperature and (b) recover essential results of exact, two-dimensional Ising model. This supports our claim of usefulness of such analytical approach, which is easy and flexible to describe different geometries (clusters, thin films) and conditions imposed on spins located on specific atoms (spins partly pinned on the surface atoms).