Instead of standing for Chief Executive Officer, it sounds like your CEO stands for Coughing Executive Officer, and that's not good for your health or corporate health. You took the right initial step by trying to diplomatically ask her to cover her mouth before going into germ-dispensing mode.
Part of the problem might be your company's sick leave policy. Employees who are sick need to be encouraged to stay home until they are healthy. If your company has placed excessive incentives on attendance, consider discussing this with management or your Human Resources representative if there is one.
Secondly, if your manager has a lingering cough, you should also diplomatically encourage her to see a doctor, or at least consider some over-the-counter cough medicines.
If none of this helps, tell your manager you need her help. When she agrees to provide it, and she will, ask her what she would do if she had a manager who came to work sick and got others sick. She will either instantly get the message or give you a strategy that will work in dealing with her. Hopefully these steps either singularly or in combination will silence the cough and the problem.
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