Mine is similar to gravy's but I used a round plate and 3 studs to hold the tire to the carrier.
Offroad Design and other companies sell the
tube and matching bushings and bolts for the upper and lower mounting points.
Even with my 35" spare there is no room for a cooler. You might be able to squeeze a gas can in if you build around it. My jack goes across the bottom just above the lower pivots.