Borges is not normally considered a very funny writer, but he had his moments.
* Carlos Argentino Daneri's truly awful poetry in "The Aleph" is funny enough in its own badness, but what pushes it over the edge is Daneri's habit of explaining at length to the narrator just how great his poetry really is, and the punchline (delivered at the end of the book) is that when Daneri finally publishes his poetry, he wins a major literary prize.
* "Pierre Menard, Author of the Quixote" is told in an entirely deadpan way, but apart from being a brilliant meditation on the meaning of authorship, the whole idea of a writer trying to write a book that already exists is very funny.