I have tried purchasing tires from Amazon Japan with a US address, which works for many other items. The order resulted in "You ordered the item below, but the package was returned to us by the carrier."
This was for IRC FB-3 tires. So it's unlikely that method will work.
Something I have had success with for importing parts (have not tried tires) is that if you find an item on Yahoo Auctions (Shopping) Japan there are quite a few forwarding services available. IMO it's not practical for tires because you pay shipping twice and would end up with a
very expensive tire where you could buy a few comparable tires available on the US market for the same price instead. If you have a friend or penpal in another country, it is MUCH cheaper to get something shipped and forwarded from them than through a service like Buyee.
e.g.
https://store.shopping.yahoo.co.jp/partsdirect/20403300.html can be purchased through
https://buyee.jp/item/yahoo/shopping/partsdirect_20403300
Another potential option is to call up your local powersports service center that does tires and ask them if they can order it in. Worth a shot. I have had luck with this for Pirelli tires that were at the time not yet available in the USA, but were in the Pirelli catalog in Italy. Local euro bike shop was able to get them in same as any other part they order, I think they ended up shipping from Romania.
My personal recommendation, find a tire from the
Tires Megathread and save yourself some $ and hassle by buying one that's available in the USA.
Shinko SR244 are a popular trail tire choice, and Shinko SR241/IRC TR-1/Kenda K262 are popular trials tire choices.