The conflict in “The Monkey’s Paw” is man versus supernatural.
There are many different types of conflict in literature. We classify man vs. nature conflicts as conflicts involving animals, the landscape, weather, or other natural forces. We classify man vs. man conflicts as conflicts between two characters. A man vs. supernatural conflict is a conflict between a character and a force of magic. That is what is happening with the monkey’s paw.
First of all, there is no monkey in the story. The monkey’s paw is a supernatural object. In other words, it is a magical object. It is an object that has had a magical spell on it, and has had magical powers granted to it. When the Whites interact with the paw, they are interacting with a magical force, and thus a supernatural force.
The sergeant-major explains the paw’s origin and story.
"It had a spell put on it by an old Fakir," said the Sargeant-Major, "a very holy man. He wanted to show that fate ruled people's lives, and that those who interfered with it did so to their sorrow. He put a spell on it so that three separate men could each have three wishes from it."
From this tale, you can tell that the paw is no ordinary trinket. It is also not really just a piece of an animal anymore. If it ever really was a part of a real monkey, that monkey part is now just a conduit for the magic that the paw contains.
The Whites were told not to wish on the paw, but they did not listen. The sergeant-major probably should not have shown it to them and told them that it could grant three wishes, because most people will not listen after that. He did warn them though.
"The first man had his three wishes. Yes, " was the reply, "I don't know what the first two were, but the third was for death. That's how I got the paw."
From this you can tell that it is the paw that the Whites really have the conflict with, not the monkey. They wish on it, and it brings them misfortune. They do get the money, but then their son dies.
If you want to consider another conflict in the story, you might say that there is a character vs. character conflict with Sargeant-Major Morris. The problem with this, though, is that he does not really do anything except present them with an ethical dilemma and then let them choose themselves. Most of the conflicts in the story are man vs. supernatural, and man vs. self. The Whites have to decide what to do with the paw. Do they wish on it, or not? The hardest wish is the third. The Whites must wish the son back to death.