Coherent backscattering of scalar waves from a semi-infinite discrete nonabsorbing random medium of nonisotropic scatterers is considered. The dependence of the line shape of the backscattering peak of the scattering nonisotropy is studied in the frameworks of the diffusion approximation. Various versions of this approximation are applied in which, in particular, the gradiental terms are taken into account, and various forms of boundary conditions are used. It is shown that the peak line shape is almost independent of the form of boundary conditions only in the vicinity of the backscattering direction. The validity of the diffusion approximation is discussed.