I dont think a tire will wobble unless the entire wheel wobbles....
Problems with the undercarraige could cause this. Also if a tire has uneven treadwear from a poor alignment, it could wobble. A missing balance weight, or improperly balanced tire could cause wobble. Emergency braking could leave a flat spot in the tire. Check all four tires for treadwear patterns, to see if the tire is balding in one section faster than others. Ideally it will bald from the center outwards evenly as the tire ages. If the tires look even, then most likely a problem with the undercarraige is causing the wheel to wobble (broken, worn or missing component). A tire could have internal belt damage from hitting a deep pot hole hard and cause it to wobble after.
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