The reason why Daily Prophet didn't write about the attacks was not explicitly mentioned in the book. So it leaves space for speculation.
The fact is that Daily Prophet was heavily influenced by the Ministry of Magic. We learn a lot about it in "The Order of the Phoenix" and further books. We don't know if Fudge was leaning on the Daily Prophet during Harry's second year at Hogwarts, but it is safe to assume he already had the power to do that.
Cornelius Fudge really wasn't a firm and confident person. He cared a lot about his image. Again we learn much about him at the end of "The Goblet of Fire" and in further books.
Already in "Chamber of Secrets" (chapter 14: Cornelius Fudge) the Minister says:
Things’ve gone far enough. Ministry’s got to act.
to do something — the school governors have been in touch —
Look at it from my point of view, (...) I’m under a lot of pressure.
Got to be seen to be doing something.
(...) Dumbledore suspended — no,
no — last thing we want just now —
See here, Malfoy, if
Dumbledore can’t stop them [the attacks], (...) I mean to say, who
I read those quotes as the information about the attacks started to spread and Fudge was expected to somehow remedy the situation. But the Minister had no other idea what to do except from counting on Dumbledore to solve the problem himself.
My conclusion is that the last thing Fudge wanted was the article in the Daily Prophet, which ould have put even more pressure on him. So the Minister could lean on the newspaper editors not to write about the attacks at Hogwarts.