In Book 19 of The Odyssey, Is Penelope being wily or does she not recognize Odysseus?
Penelope does not at all recognize Odysseus. In this same book, she hears of Odysseus being another person other than the man that she is talking to about Odysseus (who actually is Odysseus). The details help her believe Odysseus is out there, but she does not believe in his return. We know this to be true because she sets up the challenge for the suitors to compete in.
She even has a dream about Odysseus coming home and believes the dream to be untrue, just a dream, not a prophetic vision. I think what you might be referring to as wily is just the fact that the author is setting up for us and later Penelope lots of evidence for her to know for sure that when Odysseus is revealed it is actually him.