C172 Flight Instructor reported a right main tire failure resulted in a safe landing and shutdown on the runway.

Narrative

A 141 Instrument Emergencies Scenario training flight departed the ZZZ airport under a filed IFR flight plan at approximately XA:30z. Before starting the flight all pre-flight actions were completed fully and the instructor and student preformed the preflight inspection together; using the pre-flight checklist. Shortly after departure it was discovered that the right rear tire had a flat spot and the inner tube was bubbling out of the tire. During the taxi and takeoff procedures there were no abnormalities noted by the CFI or student regarding the right tires performance. As the airplane climbed in altitude it appeared that the bubble was growing in size. It was determined by the CFI to cancel IFR and begin a descent over the practice area to prevent further damage to the tire. The CFI spent time holding over the southeast practice area to determine the best course of action regarding the damaged tire. It was determined that ZZZ was the safest area to attempt a landing. The student and instructor extensively briefed the scenario; approach; and response to any abnormalities during the landing. The CFI notified ZZZ tower that the airplane was experiencing issues with the right tire and requested a landing on the largest runway available at ZZZ. The CFI preformed a soft field landing on RWY XX and was able to slow the aircraft bellow 10KT before the right tire failed. Tower was immediately notified and two maintenance personal replaced the tire while the airplane was disabled on the runway. After the tire was replaced the CFI safely taxied the airplane to the ramp. It can be noted that during the pre-flight tire inspection pushing the airplane forward to inspect the tire not visible could prevent missing any tire bald spots. There are no requirements to move the airplane forward to inspect of flat spots on the underside of the tire on the pre-flight inspection checklist.