This is an interesting question. Given the fact that Odysseus had been away from home for twenty years, and given the fact that Odysseus had left Ithaca when their son Telemachus was extremely young, we would expect that Penelope might cry quite a bit.
If one were to do a word-frequency analysis of the Odyssey, we will actually find that Odysseus cries more than Penelope does in this epic. Perhaps that should not surprise us, though, since Homer spends much more time describing Odysseus than Penelope.
Still, Penelope does her share of weeping. Early in Book 2, Telemachus tells Eurycleia not to tell Penelope of his departure from Ithaca because he does not want his mother “to spoil her beauty by crying” (Samuel Butler translation). Later, in Book 4, Athena sends a vision of Penelope’s sister to Penelope with the primary mission of helping Penelope not to cry. Still, in Odyssey 17, Penelope does weep upon her son’s return from searching for Odysseus; and, of course, Penelope weeps in Book 19, when the disguised Odysseus tells her tales of Odysseus. Also, in Book 19, Penelope also tells the disguised Odysseus about a dream she had in which she was weeping in her room. Finally, after Penelope hears Eurycleia’s news that Odysseus has slaughtered the suitors, then she “wept for joy” (Samuel Butler translation).
So, in sum, I think it is safe to say that Penelope does cry a lot in the Odyssey. Who can blame her, though; she’s been through a lot.