To open this demon door, it wants acts of love and kindness. The easiest way to do this is to either bring a coop partner, or use a second controller profile, and propose and marry the person in front of the demon door. You’ll need the Family and Lover Expression Pack from the Road to Rule to do that though.
Alternatively, you can go through all of the positive expressions to your partner in front of the door to make it open. Obviously this method is the much easier option.