  $2p$-based magnetic moments and magnetic coupling are studied with density
functional based methods for substitutional N in the alkaline earth monoxide
series MgO, CaO, SrO, BaO. The hole is rather strongly localized near the
N$^{2-}$ ion, being somewhat more so when strong on-site interactions are
included in the calculations. Strong magnetic coupling is obtained in the
itinerant electron limit but decreases strongly in the localized limit in which
the Coulomb repulsion within the N $2p$ shell (U) is much greater than the N
$2p$ impurity bandwidth (W). We find that this limit is appropriate for
realistic N concentrations. Ordering on a simple cubic sublattice may maximize
the magnetic coupling due to its high directionality.
