Interesting, the period 1A.D. to 500A.D., is known as Kofun period. This was when people were buried in mounds often with treasure. This idea came from the Asian Continent, which in turn had periods in which the Sakas from Central Asia and the Roman Empire traded with the China (via Parthian and other intermediaries) over the Silk Road. Make an interesting fantasy/adventure book.
I think they might have arrived there through trade. Arabs used to trade with China, Singapore, today's Indonesia... in the middle ages and perhaps even before. I think that the Japanese might have bought those coins or received as an exchange or gift from traders in Asia or, from European traders.
From the info that the coins were made when Constantine l was Emperor, This would infer a time around 270 - 290 AD. The Han Dynasty had disappeared & the Middle Kingdom was fragmented into the three kingdoms. Trade between european traders and China was almost non-existent. More likely the Persian Empire & Sakas were responsible for the coins traveling to China & then on to Japan. This period was marked by many wars & trade was often fraught with danger.
Roman coins are occassuonally found from secure archaeological contexts in Ireland (which was never part of the Roman empire). Explanations include trade, returning Irish mercenaries, visiting Roman merchants and curiously Roman tourism. Those who could afford and had the interest travelled widely, and even back then it appears they had the custom of tossing a coin in the fountain/lake/pond for good luck. Plenty of fuel for historical fiction indeed...
