A two-dimensional (x, z) particle simulation model based on the Darwin approximation to Maxwell's equations is developed for studying collisionless reconnection in the magnetotail. The particles and fields are initialized in accord with a general equilibrium configuration which includes a pressure gradient along the tail axis and tail flaring. The model is used to investigate a number of theoretical issues regarding the spontaneous ion tearing instability under the assumption that the electron dynamics are unimportant. It is demonstrated both numerically and analytically that in a thin current sheet with ρ i0 ∼ λ (ρ i0 is the ion Larmor radius based on the lobe field and λ is the characteristic thickness of the current sheet) the growth rates in the absence of a normal field component are much smaller than expected based upon the analytic theory for a thick sheet (ρi0 ≪ λ). For such a thin current sheet the presence of a normal field Bz on axis of even a few percent strongly inhibits the growth of the instability. This result is not altered by the addition of a constant By component smaller than the lobe field. It is demonstrated further that the transition to stability occurs when the cyclotron frequency based on Bz equals the growth rate of the Bz = 0 tearing mode. This requires typically a normal field of the order of 6% of the lobe field. If a sufficiently large external perturbation of the lobe magnetic field reduces the normal field on axis below the stabilization threshold over a significant fraction of a tearing mode wavelength, then one can recover the rapid instability of the one-dimensional neutral sheet.