You also should be aware that there is a difference between "split rims" and "multipiece rims" or wheels.
Most heavy vehicle people think of the Firestone RH-5 design when you say "Split" because they are split right in the middle -- you can usually spot them because they have a hump and a seam in the middle of the wheel. They are truly dangerous and most shops are prudent not to work on them.
"Multi-piece" wheels, which you most likely have (by the way, are they Daytons or Budds ??), are solid wheels that use a locking ring on one side to hold the tire bead. They are used with tubed tires. They are safe and good wheels as long as they aren't damaged or rust pitted.
Are your axle hubs spoked or do they have 10 or so lug nuts? If your axles have spokes that hold the wheels, those are called "Dayton" wheels. If they use lug nuts like a car, they are called "Budd" wheels. There are other styles of the lug nutted wheels, but they are generally called Budd wheels.
Most tire shops that handle large commercial trucks or farm equipment will deal with a multipiece wheel. They may fuss a little but they will.
It is possible to find either single piece Daytons or Budd wheels to fit your axles. It may require tripe to junkyards that have commercial vehicles or old school busses. Make sure you know your hub diameter and lug spacing (if Budd wheels) or your diameter and width (if Daytons).
Also make sure you know if your Budds (if you have Budd wheels) are stud piloted or hub piloted.
This all may seem overwhelming at first. And it was for me a long time ago, but these are the things you should know before you go tire and wheel buying/modifying/upgrading.
In the meantime, if you have locking ring/multi-piece wheels, and they aren't damaged or rust pitted in the bead ring area, you should be able to get new replacement tires and drive on while you do your research for the set of tires *after* that.
Have fun!