An Ising spin model for the magnetic phase of YBa₂Cu₃O_6+x (123) is studied with Monte Carlo simulations. The existence of frustrated spin couplings is shown to play an important role in the spin ordering. The specific heat, magnetic order parameters and susceptibility are calculated for various values of x. The deduced magnetic phase diagram is in good agreement with experimental results, showing the interplay between type-I and type-II antiferromagnetic orders. The relevance to a variety of doped 123 materials is discussed with a more general three-dimensional phase diagram.