We know that Harry's introductory letter from Hogwarts arrived some time before his birthday, but after he had already been accepted at the school Vernon and Petunia had picked out. It's possible that first years get their letters sooner than other years, to accommodate first time attendees.
In Book 2 Harry and Ron receive their book lists on an unknown date. Harry asks if Ginny will be attending Hogwarts as well. Ginny nods in confirmation, but it's possible that having six other siblings who have already attended is what makes her certain, rather than having already received her own letter.
In Book 3 Harry receives, on his birthday, a 'thicker than usual' letter from Hogwarts, which states that his book list and Hogsmeade permission form are included.
In Book 4, school supplies are not mentioned until after the World Cup, which seems to have been in mid-August.
Book 5 is an oddity. The students don't receive their lists until the last day of their holidays. Ron mentions he was worried they would never show up, as they "usually come much earlier than this." There is a possibility that Grimmauld Place, being the Order's headquarters, has some extra magical protections that delayed the owl delivery, but given that owls themselves have magical delivery powers of their own, this is only a vague guess.
Book 6 only mentions that OWL results came in the day after Harry and Dumbledore recruited Slughorn into teaching.
Are there any other sources or information that could indicate exactly when Hogwarts book lists are sent out? Or does Dumbledore, being quirky but also a bit careless, just send them out whenever he feels like it?