While you cannot turn bad news into good through clever wording, the way that you deliver bad news in writing can affect how it is received the same way that it does when speaking. Some speakers know how to deliver bad news, and others only make it worse. The same is true in writing.
The introduction is very important. It sets the context for the bad news, and context has a lot to do with how bad news is received. Instead of jumping straight into the bad, try leading with something positive. Describe what went well. Or explain something positive about the future. Take the long term view, and present a positive vision for the future.
The bad news itself should go in the middle of your message. If there are 5 paragraphs, the bad news should hide in the middle of the third. Your goal is not so much to hide or minimize the fact of the bad news, so much as it is to place it in context and make it part of an overall message. Once delivered, the bad news should be followed by the remedy, lesson learned, or course of action that will result in future prevention or improvement. You should consider making a commitment to turn a weakness into a strength. However, your response must be credible and verifiable.
Conclude by showing that you care. It could be nothing more than an apology, but it should show genuine empathy. You have mastered the art when your handling of the situation earns you respect and you are seen as someone who can be relied on when things go bad. And it's OK to tell the reader that this is what you hope will result in the long run. You want your reader to recognize that everyone has to deliver bad news sometimes, that you are making an effort to do it right, and that if the shoe was on the other foot, they would be saying and doing the same things.
The key to delivering bad news is trust. When you have bad news to deliver, it often means that your trust has already been damaged. If your message is not credible or you fail to live up to your commitments to make positive changes, the result can make things worse instead of better. If your delivery of bad news is deceitful or lacks credibility, it will be like pouring gasoline on the fire. If the reader's trust in you is damaged, it can be earned back, but only if you are willing to make the effort.