In the case of a damaged business reputation, the goal of the business in question would be to restore, as soon as possible, the public's positive opinion. By far the most effective form of promotion that could be used to accomplish this would be public relations.
Other promotion types, such as advertising, direct marketing, or sales promotions, do not get to the heart of the issue: why the customer should again trust the business. A damaged reputation will not be amended with simply a clever advertising idea or a good sales pitch. Rather, the business must focus on restoring the reputation they had previously or on building a better one, and the only way to do so effectively is via direct contact with the customers.
The meaning of the term "public relations" is basically to inform potential customers about the company and to persuade them, if at all possible, to have a favorable view of it. This involves understanding well what people want and expect from the business, addressing their concerns, and using publicity effectively to generate interest in the company. When used skillfully, this form of promotion can do much to correct a damaged business reputation.