I had the same problem a couple of month ago. Most 4" tires online will look too narrow on the 4" rim.
I bought these on Amazon MaxAuto 11x4X4 11x4.00-4 Turf Saver Lawn & Garden Tire P512 LRA, Set of 2
These are a half inch taller 11" total so make sure you have enough room between the rim and fender. I did not have any issues. However, the 2-speed clutch is close to the tire.
Side note: Make sure the steel bearing spacer is not missing that should be between your two-piece 4" rim.