Santa Dave,
The coehorn mortars use a simple solid oak block "bed". John Muller's "Treatise on Artillery" lists the appropriate sizes for coehorns. I've give you the demensions he lists for a 4.6 inch bore size (12 pdr)mortar and maybe you can scale it down to the bore size of your tube.
Length - 28.5 inches
breadth - 14
hiegth - 9
lenght of tube cavity - 5.7
trunnion cut, end to end - 11.7
trunnion hole depth - 2.2
trunnion hole diameter - 2.4
The tube was locked in the bed at a fixed elevation of 45 degrees. The range was adjusted by powder charge.