  We present studies of an effective model which is a simple generalization of
the standard model of a local pair superconductor with on-site pairing (i.e.,
the model of hard core bosons on a lattice) to the case of finite pair binding
energy. The tight binding Hamiltonian consists of (i) the effective on-site
interaction U, (ii) the intersite density-density interactions W between
nearest-neighbours, and (iii) the intersite charge exchange term I, determining
the hopping of electron pairs between nearest-neighbour sites. In the analysis
of the phase diagrams and thermodynamic properties of this model we treat the
intersite interactions within the mean-field approximation. Our investigations
of the U<0 and W>0 case show that, depending on the values of interaction
parameters, the system can exhibit three homogeneous phases: superconducting
(SS), charge-ordered (CO) and nonordered (NO) as well as the phase separated
SS-CO state.
