Any time of year is a good time to sell coins on Ebay: there doesn’t appear to be any strong seasonal cycle in demand, at least for the broad category of “coins”.
We derive this from looking at Google search data. The plot above shows the number of searches for “Ebay coins” over the course of one year. People are searching for coins on Ebay approximately as much in January (the start of the graph) as they are in July (the middle of the graph).
We also have info on the best time of year to sell other things on Ebay, too.