Explain how the supernatural appears in "The Rime of the Ancient Mariner" and "Goblin Market."

Although "The Rime of the Ancient Mariner" and "Goblin Market" contain supernatural elements, they represent different literary genres. Coleridge's poem is Gothic, while Rossetti's poem is a fantastical allegory.
"Rime" includes polar spirits who wreak judgment on the sailors for the death of the albatross and require penance of the ancient mariner. Coleridge's glosses, added for later versions of the poem, explain that the sailors "become accomplices of the crime." When the ship gets stuck in the doldrums, the "Albatross begins to be avenged," presumably by the polar spirits mentioned in line 132. The next evidence of supernatural influence on the ship occurs when the Death Ship arrives, containing Death and "the Night-mare Life-in-Death." Death takes the mariner's shipmates while "Life-in-Death begins her work on the ancient mariner." In Part 5, after the mariner has partially redeemed himself by blessing the water-snakes, the dead men are inhabited by "a troop of spirits blest" that sail the ship. In Part 6, the Voices, presumably of the polar spirits, converse. After the "seraph-band" departs, the ship sinks supernaturally at line 546. Thereafter the mariner falls into a supernatural "agony" when he needs to tell his story, and the listener is held in a supernatural spell that forces him to listen.
In "Goblin Market," the goblins are supernatural creatures in that they cannot necessarily be heard or seen by people. After Laura eats of their fruits, which have supernatural powers, she finds she can no longer hear or see the goblin men. Lizzie, however, in her undefiled state, is still able to "hear the fruit-call." The fruit's supernatural effect is to gradually drain the life and passion from the one who eats it until the person dies, as happened to Jeanie. Laura begins to supernaturally waste away, and Lizzie goes on her mission to save her. She comes back with the juice on her face without having consumed any fruit herself. Lizzie implores Laura to "suck my juices," and when she does so, Laura makes a supernatural recovery overnight; in the morning she "laughed in the innocent old way." Laura and Lizzie, when they become mothers, warn their children of the "haunted glen" and of the power of self-sacrificing sisterhood. 
In both "The Rime of the Ancient Mariner" and "Goblin Market," supernatural beings seek to do harm to the human protagonists. In each case the humans learn an important lesson, and in each case they become evangelists of sorts, although only in "Rime" does the evangelism retain a supernatural component. Both poems incorporate supernatural elements, although Coleridge uses a Gothic approach while Rossetti uses fantasy and allegory.