There are many references to Charon and the fee of the ferryman for passage of the dead from the 5th century BC. The earliest mention of the story is found in:
Pindar, Fragment 143 (Greek lyric 5th B.C.)
Timotheus, Fragment 786 (Greek lyric 5th B.C.)
Aeschylus, Seven Against Thebes (Greek tragedy C5th B.C.)
also Euripides, Aristophanes,
Plato and Callimachus make mention of the Charon myth, asserting that the story was well established in the 5th century BC.
The timeframe of the custom of placing an
obol in the mouth of the deceased is another matter. I have yet to find any ancient eastern references to the custom or the story. That is to not say they do not exist, but I cannot find any. It could very well be that the silence on the subject could prove to mean that the eastern Asian custom did not exist in early
antiquity. This is why I assert that the custom probably originated in ancient Greek culture.
I would love to be proved wrong on the matter and find that an eastern culture
had such an influence on the Greek mindset and religion as to transfer a funerary custom to the Hellenistic world. If you know of any other reference material on the subject, please let me know!