Directly, once. This incident occurs after he finds Jenni committing adultery. Oscar drinks heavily and then decides that due to the curse (fuku), he should throw himself off a bridge.
However, depending on your viewpoint of what constitutes an "attempt," that number might increase. If you consider his insistence near the end of his life to be desiring of death--his answer to the Mongoose, for instance, being "more" indicating that he will push until he is destroyed--then it might be the case that his murder could be viewed as a successful suicide attempt. However, this would require a great deal of searching for evidence from the text.