The influence of ion-neutral interactions ͑charge exchange, elastic scattering͒ on scrape-off-layer ͑SOL͒ stability is studied in the eikonal limit for a single-null X-point geometry typical of tokamak divertors. Instability drives due to curvature and to the ion-neutral drag effect are included in the model. The ion-neutral interaction terms are highly localized near the divertor plates; these terms are stabilizing for typical parameters and large enough to affect the SOL ballooning-interchange stability in the absence of resistivity. It is shown that the growth rate of ideal curvature-driven modes is significantly reduced by the ion-neutral interaction terms; the growth rate of resistive ballooning modes is not affected much by the neutrals, because resistivity allows the mode to disconnect from the divertor region. In both cases, the X-point geometry significantly affects the stability. An ion-neutral drag instability localized near the plates is only found in a small region of parameter space. Conditions for the existence of this instability in X-point geometry are discussed.