Hi - You will find songs about La Llorona in this thread (click), and Google will take you to many stories about her. The Wikipedia article is particularly interesting. I found one at http://www.americanfolklore.net/folktales/nm3.html:

La Llorona
retold by
S. E. Schlosser

Version I

Once there was a widow who wished to marry a rich nobleman. However, the nobleman did not want to raise another man's children and he dismissed her. The widow was determined to have the nobleman for her own, so the widow drowned her children to be free of them. When she told the nobleman what she had done, he was horrified and would have nothing more to do with her. As she left him, the widow was overcome by the terrible crime she had committed and went to the river, looking for her children. But they were gone. She drowned herself and her spirit was condemned to wander the waterways, weeping and searching for her children until the end of time.