Five years ago, I wrote a perfectly inadequate answer to a related question about this practice in the American West:

There are a lot of websites on this but none is definitive; this one is of interest. In general, we can say that the practice is widespread, functionally, as a means to keep the eyelids from snapping open after death. The coins are often fused in the popular mind with the coin placed in the mouths by the ancient Greeks, providing payment to the ferryman to cross the river into Hades. That connection may or may not be valid. What is clear is that other cultures did this before the settlement of the Old West.

Looking back on this and reconsidering the question, I would say that the practice of coin use and the dead does not originate with ancient Greek tradition but rather it is also expressed by ancient Greek practice. I doubt we're looking at diffusion from the ancient Greeks. Rather the association of coinage and the dead appears to be widespread and part of a broad folk tradition.

Placing coins or other objects on the eyes has a practical purpose - keeping the eyes from involuntarily fluttering open as part of the mortification process. Giving something valuable to the dead is also a widespread process.

The introduction of coinage - historically and as part of geographic diffusion - created a great deal of popular fascination, and coins quickly worked their way into many people's local folklore in a variety of ways.

An article by Charles Francis Potter, in Funk & Wagnall's Standard Dictionary of Folklore, Mythology, and Legend (1949) does not take this any further. I couldn't find anything better with an internet search (except to find my own inadequate five-year-old answer!). Clearly, more needs to be done here!