Just some other options:
Spartan Mowers and Bad Boy Mowers both come with "special" tires that are supposedly only made for them, but Kenda makes the ones for Bad Boy (called "Reaper", bias-ply, Kenda K3012). If you check ebay and search for something like "Bad Boy tires" with your size you can find them. Here is just 1 example:
Find many great new & used options and get the best deals for (2) Reaper K3012 HD Tire Assemblies 24x12.00-12 Bad Boy Outlaw 54" 022-4050-00 at the best online prices at eBay! Free shipping for many products!
The Spartan tire tread is radial and looks like this:
I haven't found the manufacturer but you can buy the tires online at the above link or at your local Spartan dealership.