I have been able to find only three companies selling solid-core Urethane Airless No Flat Tires/Air Free tires. Sorry about that!

1. AIR FREE TIRES   Another solid core tire company. Airless tires.
    
2. GREENTYRE   Tyres without air. Solid core tires.
    
3. AMERITYRE   Solid core tires. Airless tires. They have some road tires but mostly off-road type tires.