Should be a cheap repair.
Without a video or a more accurate description it's not possible to tell what the problem is, but to start it's not the TIRE that's wobbling. Tire refers only to the rubber portion that meets the road. The entire assembly is a wheel, the outer band of metal that the tire mounts on is the rim. Google "bicycle parts diagram" for more info on terminology. "Wobble" is usually used to describe back and forth motion in either the rim or freewheel when the wheel is turning.
If you can take the rim and shake it side to side when it is not moving it has "play" in the bearings, indicative of bearings that are not properly adjusted, worn or both.
If the rim wobbles back and forth while the wheel is turning the spokes need adjustment.
If the cog/freewheel wobbles back and forth when the wheel is turning it's related to either a bent axle or a hub that just is not perfectly machined (not unusual)