For what it's worth, plain old tires (not mounted on rims, and not inflated) are not even mentioned in the IATA Dangerous Goods Regulations (DGR). This means that from a shipping point of view, you can ship as many of them as you want, without restriction.
Some air carriers have their own prohibitions against shipping automobile parts because the parts themselves can contain flammable liquids, corrosive chemicals, things like that. But, it should not be too difficult to convince someone that a motorcycle tire is not an 'automobile part'.
However - if the tire is mounted on a rim (a wheel) such that it could possibly contain air under pressure, then that is another matter altogether. The IATA DGR permits tires that are mounted and inflated 'to not over their maximum rated pressure', but forbids mounted tires that have any kind of damage (plain old tread wear could be considered damage) and forbids mounted (built-up) tires and rims when it is not possible to establish both the pressure of the tire and the allowable maximum pressure of the tire.
So - to avoid problems, don't ship the tire mounted on a rim, ship it by itself. Maybe wrap some evergreen boughs around it, and declare it as a Christmas wreath.
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