Spoiler:
Littlefinger framed Tyrion. iirc he gave the knife to King Robert. As for who tried to have Bran killed, the main psychopath in the story of course! Or at least it's implied. King Robert was talking to Cersei about it would be a much kinder fate for Bran to have died of his fall, within ear shot of Joffrey. Joffrey wanted to show his father he could do it. He stole the knife from Robert's armory thinking no one would know about it.

