Stir together salt, brown sugar, cumin, coriander, paprika, and pepper in a small bowl. (If necessary, remove giblets from chickens, and discard or reserve for another use.) Sprinkle skin and cavities of chickens with salt mixture. Chill, uncovered, at least 8 hours or up to 24 hours.

Preheat a gas grill to medium (350°F to 400°F) on 1 side. Open beer cans; pour out 1/2 cup beer from each can. (Drink the poured-out beer, or reserve for another use.) Working with 1 chicken at a time, hold chicken upright with cavity facing down, and insert 1 opened beer can into cavity. Pull legs forward to form a tripod, allowing chicken to stand upright.

Place chickens upright on unoiled grates over unlit side of grill. Grill, covered with grill lid, until the skin is crispy and a thermometer inserted in thickest portion of thighs registers 165°F, about 1 hour, 40 minutes. Remove from grill; rest 10 minutes. Carefully remove cans; cut chickens into quarters.