Three-dimensional equilibrium solvers have been extensively used to investigate stellarator equilibria, but it was only recently that they have been adapted to model the magnetic diagnostics on a functioning experiment. The paper presents the new computer code NEMEC-DIAGNO which was written to model the diagnostic coils on the W VII-AS stellarator. This code extends the free-boundary equilibrium solver NEMEC to calculate the magnetic field and the vector potential due to the plasma currents alone and incorporates detailed models of the coils themselves. In its application to W VII-AS over a range of its operation, the code yields a set of simple curves which provide a prescription for finding the average plasma beta under varying conditions of pressure profile and net longitudinal 'bootstrap' current.