How should one cite the entirety of a journal?
There are certainly interesting kinds of research where you would do this, such as bibliometrics, meta-analyses, history of science, intellectual history, or a subject bibliography.

The APA style blog opines that you would not need to make the actual citation for a meta-analysis: rather, you would simply mention the names of the journals (and the time periods you survey) in the text.

However, let's say you're looking at periodicals that are hard to locate today. Then a citation should help the readers find them. If they all came from the same database or archive, then perhaps it would make sense to cite that database or archive itself in the bibliography, with a mention or footnote about which journals were in which database or archive. Here's a page showing how to cite a collection of institutional records.

Or, if you're doing more of an intellectual history, you may be able to mark the beginning of each journal by citing the opening editor's note. 

Then again, JSTOR allows people to download some journal information for research purposes. JSTOR's metadata fields for journals are journal-id (along with an identifier of who assigned this unique id), ISSN (possibly more than one if it changed over time), journal title (as of the time period you are discussing), and the publisher (as of the time period you are discussing).

Again, if you're doing a meta-analysis, the journals are part of the methodology but you probably don't need to fully cite them if they are current, modern journals.  If you're doing more of a history or a source bibliography, then you might just have a long "bibliographic note" appendix describing the journals, including where to access each and a history of changes to the names and publishers. 

If all else fails, this is quite an ad-hoc citation, but you might try to find (or build) a reference type that uses the following:

Title: journal title

Publisher: publisher (might use organization field for this if there is no publisher field)

Organization: organization creating the journal (if available)

Address: city of publisher

Identifier number: ISSN (if available)

Year: Span of years

Archive: (database or archive info)

Location in archive: URL, shelf number, etc.

Note: How often is/was the periodical published; anything about disruptions to the run.



Update: If the otherwise best format requires an author/editor, you could use the name of the organization that created the journal, which is often promoted to "author" in the absence of a single author or editor. If that is not applicable, you might be able to use the name of chief journal editor(s).  You would want to make a note somewhere that you chose to record the information (editor, publisher, journal title, association, etc.) as of X date (journal founding, first issue in your time period, last issue in your time period, as of a given date across all the journals you're looking at).

Mendeley's Ultimate Citation Cheat Sheet might help you figure out desired formatting for your substituted-in components in the style you're using. It covers MLA8, APA, and Harvard, and if you're using a different style that might help you abstract the principles to that other style, if there is not sufficient documentation on that style's principles.