Assuming no indication of spinal or head injuries, I'd use a coma or "side-stable" position if they were unconscious, or any position that allowed the head to turn so vomit would drain away and not be aspirated if conscious. I'd also consider raising the legs above the level of the heart to autotransfuse more blood to the core.
Dark, granulated vomit is likely to be lysed blood from a gastrointenstinal bleed (stomach or lower GI would be my guess, from the "coffee grounds" look of the blood vice something red or tarry). Id this is the case, they're very likely tol vomit again, and aspiration of the vomitus can be extremely dangerous.