Do you know that it is kunyomi or do you assume so just because "go' is also onyomi? It's not a binary thing. There are often more than one Chinese pronunciation for the same character, and thus more than one possible onyomi reading.
Nelson's has "a(i)" as kunyomi, "go" as onyomi. Nelson's is pretty limited and incomplete, though, so let's check some Japanese language dictionaries.
The Obunsha Kanwa Jiten (a modern Japanese - Chinese dictionary) has "go", "katsu", "gatsu" and "kou" as onyomi, and a(u) and a(i) as kunyomi.
The Kanjigen (basically a Japanese dictionary of classical Chinese) has the same as the Obunsha.
So you're right. *I* don't know for a fact that "ai" is kunyomi. But those arrogant Japanese sure seem to think *they* do. It is their language, so I'll defer to them.