a 31 x 9.5 x 15 tire does not seem to exist
a 31 x 10.5 x 15 tire needs a 7"-9" wide rim
a 30 x 9.5 x 15 tire needs a 6.5" - 8.5" wide rim
This is from Tire Rack, some shops will only follow these guidelines other don't care.
If you are looking for a steel rim, Summit sells Wheel Vintiques which I have used...
https://www.summitracing.com/parts/WVI-62-575504