In order to answer this question, let's first examine what those literary terms mean.
A protagonist is usually a main character of a literary work who faces a significant source of conflict. The antagonist works against this main character and is often thought of as the "villain," though in more complex plots, this isn't always the case.
If we apply these definitions to Lord of the Flies, we can recognize Ralph as the protagonist. He is a main character, and readers become invested in his struggle to maintain much-needed order on the island. His primary opposition is Jack, who represents savagery and generally stands in the way of all Ralph attempts to accomplish.
Piggy doesn't fall neatly into either of these definitions, and it's important to recognize that not every character in a story is either a protagonist or an antagonist. Some characters further the plot and therefore have a valuable place in the story but stand outside the central conflict. Since Piggy aligns himself with Ralph and the desire to maintain some semblance of civilization on the island, he can't be an antagonist based on our definition. He would more closely resemble a protagonist because of his symbolic representation of wisdom and intellectualism, though he is not as central to the conflict as Ralph is. Piggy is a source of support for Ralph as they stand together in opposition against Jack's barbaric and chaotic actions.