This page on the Chinese Embassy in Dublin explains that one has to apply in person in the Dublin office, or send somebody else. In other words, the postal system here is considered so undependable by the Chinese authorities that they're not going to risk using it!
Holiday visas last for 3 months from time of issue. This means that in order to get the visa for myself, my wife and the two kids, we're going to have to head up to Dublin within two months of departing Ireland. What a pain in the ass!