Any chance of a photo of the tire you are looking for?
A drawing in the repair manual suggests a profile similar to a wheelbarrow tire with circumferential rib/groove tread.
A cursory Google suggests the size is used on lawnmowers, handcarts go-karts and (ultralight?) aircraft.
http://www.lawnmowertirestore.com/3-...-and-tube.html and
http://www.aircraftspruce.ca/catalog...SABEgLBI_D_BwE PLy ratings and weight capacities seem to vary with most of the Google results having squarer shoulders than the manual seems to be showing.
Also, what weight capacity do you need? Google was showing a range from 380 to over 450 pounds.