I like to collect diaries but I couldn’t find any word for this hobby nor for what a collection of diaries is called. If anyone knows please share.
If you are looking for a word like Numismatic ( of coins ) there isn't one, however that doesn't mean we can't invent one:
Using the same etemological rules as Numismatic and Numismatist, let's construct a new word.
We shall say Ephemerismatic (of diaries) and Ephemerismatist.
So you are an ephemerismatist and you are interested in ephemrismatics.
It appears that archive is the term officially used also for diaries:
Interview With Sally Macnamara, Collector of Handwritten Diaries Not long ago I started corresponding with Sally Macnamara Ivey who has collected and sold diaries since about 1987.