Who is the protagonist of "Tennessee's Partner"?
The protagonist is the principal character. What that means is that the protagonist is the person most affected by the conflict of the story. The conflict of this story is internal - man vs. self. The protagonist, Tennessee's Partner, has to weigh the actions of Tennesse against his loyalty to his friend. Throughout the story, Tennessee tests the friendship, stealing the Partner's wife, being a theif, etc.. However, the Partner will not allow it to break the bond between them. The Partner - when confronted with the conflict - chooses loyalty. This choice is the climax of his conflict, and the resolution is that the bond remains intact even beyond death.
It should be noted that picking a protagonist can be tricky. Some would assume that the narrator of 1st person point of view story is the protagonist - he's telling it, its his story - we can see here that this is not always the case. The narrator of this story has very little to do with it. Likewise, title characters are not always the protagonist. It is true here, but in a novel such as "The Great Gatsby", it does not hold true (the protagonist there is, in fact, the narrator).
The protagonist of any story is the main character in that story. As the Guide to Literary Terms says, "This is not always the hero, but is always the principal and central character whose rival is the antagonist."
Given that definition, then the protagonist of "Tennessee's Partner" has to be the title character himself: Tennessee's Partner.