Any work that is protected by U.S. copyright law can be registered. This includes many works of foreign origin. All works that are unpublished, regardless of the nationality of the author, are protected in the United States. Works that are first published in the United States or in a country with which we have a copyright treaty or that are created by a citizen or domiciliary of a country with which we have a copyright treaty are also protected and may therefore be registered with the U.S. Copyright Office. See Circular 38a, International Copyright Relations of the United States, for the status of specific countries.
Minors may claim copyright, and the Copyright Office issues registrations to minors, but state laws may regulate the business dealings involving copyrights owned by minors. For information on relevant state laws, consult an attorney.
You can register copyright in the diary only if you own the rights to the work, for example, by will or by inheritance. Copyright is the right of the author of the work or the author's heirs or assignees, not of the one who only owns or possesses the physical work itself. See Circular 1, Copyright Basics, section “Who Can Claim Copyright.”