Final answer:
The item in The Binding of Isaac that increases your chances of finding an Angel Room instead of a Devil Room and is also the second half of the key required to enter the door to the Mega Satan boss is Key Piece #2.
Step-by-step explanation:
The item in The Binding of Isaac that increases your chances of finding an Angel Room instead of a Devil Room and is also the second half of the key required to enter the door to the Mega Satan boss is Key Piece #2. It drops from one of the angels that appear when you bomb the statue in an angel room.