How do I cite an unpublished material (e.g. diary) in Chicago Style?

Chicago Manual of Style (CMOS)  14.221:

Full identification of most unpublished material usually requires giving the title and date of the item, series title (if applicable), name of the collection, and name of the depository. Except for placing the cited item first [in a note], there is no general agreement on the sequence of the remaining elements in the citation.  Whatever sequence is adopted, however, should be used consistently throughout the same work.

Citations of collections consulted online will usually take the same form as citations of physical collections, aside from the addition of a URL or database name.

Elements of footnote:

Title of cited item, format (e.g. original manuscript, digital reproduction of original manuscript, transcript), date of item (unless clear from the title), box number (if applicable), name of the collection (if applicable), name of the depository.

(Include the page number if the source has page numbers, e.g. the transcript, the pdf version of the original – see examples below.)  

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Elements of bibliography:

Title of item cited. Format. Date of item (unless clear from the title). Name of collection (if applicable). Name of depository.

Note: don’t use italics for the title in either the footnote or bibliography.

Footnote examples:

2. Mary Ann Friend Journal Typescript, n.d., State Library of Western Australia, 19, https://www.slwa.wa.gov.au/sites/default/files/MaryAnnefriendtypescript.pdf.

3. Mary Ann Friend's Journal of a Voyage to Hobart with Account of the Settlement on the Swan River, 1829-1831, digital reproduction of original manuscript, State Library of Western Australia, 34,  https://www.slwa.wa.gov.au/sites/default/files/MaryAnnFriendDiary.pdf.

Short form footnote examples:

6. Journal Typescript, 20.

7. Mary Ann Friend's Journal, digital reproduction, 35.

Bibliography examples:

Mary Ann Friend Journal Typescript. n.d. State Library of Western Australia. https://www.slwa.wa.gov.au/sites/default/files/MaryAnnefriendtypescript.pdf.

Mary Ann Friend's Journal of a Voyage to Hobart with Account of the Settlement on the Swan River, 1829-1831. Digital reproduction of original manuscript. State Library of Western Australia. https://www.slwa.wa.gov.au/sites/default/files/MaryAnnFriendDiary.pdf.