Magnetic phase diagrams of disordered Heisenberg antiferromagnets with mixed uniaxial anisotropy are calculated within a local molecular field theory. The phase diagrams numerically obtained for sets of parameters relevant for the system Fe_1-xNi_xCl₂ are in very good agreement with recent experimental results. It is demonstrated that by changing the concentration x, or the ratio of the anisotropies, a rich variety in the physical behaviour of these systems can be expected.