The letter should be clear and concise and although the issue is one that is personal, you should try to keep the language and information to a professional standard. This means that you should not go into too much detail about your reasoning and, if you do not feel that there is anyway that you can make the meeting, make it clear that this is your stance. If the cancellation is left open to negotiation and you are persuaded to attend it, canceling again at a later date will look even more unprofessional.
Try to rearrange the meeting or at least suggest when you will be available to meet the person again. Do not leave it too long but obviously do not suggest a time period that you do not think you will be ready in. Remember that the person you are meant to be meeting will be understanding. You do not have to try to justify yourself too much as it is something that everyone has to deal with.
Your letter could read as follows:
"Dear [insert name], I am writing to inform you that I will not be able to attend our scheduled meeting on [insert details] due to a death in the family. I will be available to reschedule the meeting from the [insert date] onwards and I hope that we can organize it soon. I am sorry for any inconvenience that this may have caused. Yours sincerely."
Make sure to date the letter that you send and include any contact information that you would like the recipient to use.