Here's a quotation from the [Harrisburgh] Pennsylvania Reporter, reprinted in the Political Register (December 24, 1832), on the subject of South Carolina's pursuing the possibility of nullifying its membership in the United States:
The ordinance and address recently adopted and put forth by a Convention of nullifiers in South Carolina, has awakened among all classes of citizens, and all political parties, in the commonwealth [of Pennsylvania], the most lively indignation. Both the ordinance and address are deeply imbued with treasonable sentiments, and fraught with doctrines as strange as they are dangerous and intolerable. This state of things cannot much longer be endured. It is of the very last importance to preserve the union of the States, and while we regret that citizens so illustrious for talents as many of the leading nullifiers unquestionably are, should, bu an unaccountable infatuation, bring upon themselves the deep and damning infamy that is ever coupled with the name of treason, we do not hesitate to declare that, in our opinion, we have already conceded enough for purposes of reconciliation, and that it is high time to resort to means more effective than argument and persuasion, to put a stop to the high-handed measures, and quell the rebellious spirit of nullification. However much and deeply we should deplore an appeal to arms, as involving the most dreadful consequences, the time seems to have arrived when such a measure can alone save the republic. To tamper longer, is to hold out encouragement to rebellion, and endanger a Union, upon the existence of which depends the happiness of unborn millions in this land, and the success of free institutions throughout the world. Let all parties be united and speak with one voice upon this subject, and let their language be, "The Federal Union—it must and shall be preserved." To effect so great an object, every citizen should be ready and willing to "pledge his life, his fortune, and his sacred honor."
Then follows a comment by the editor of The Political Register:
Little does the editor of the Reporter know of the feeling in the south if he supposes that such language [as the Reporter's call to arms to preserve the United States entire] has a tendency to preserve the Union! He has indeed profited little by the lessons of history, if he supposes that South Carolina is to be subdued into an acquiescence in the protective system. Who supposes that this Union is to be maintained by force?
As the excerpts show, there is some inconsistency in the periodicals' handling of the word union. The Pennsylvania Reporter lowercases the term when referring to "the union of the States," as though interpreting union in that setting as a descriptive term meaning something like "continued unity or conjunction," but capitalizes it when using "a Union" to allude to the United States and when referring to President Andrew Jackson's famous toast of April 13, 1830, to "the Federal Union" as a political entity. The Political Register, meanwhile capitalizes Union both when saying "the Union" (that is, the United Sates) and when saying "this Union" (again the United States).
From this evidence, I conclude that people before the Civil War were to some extent accustomed to seeing "the Union" used as an alternative designation for "the United States," and that it would be reasonable to capitalize it today just as it was capitalized then—and after the Civil War.
The case for northern and southern is far less clear, as the only instance in the excerpts is to "feeling in the south." Elsewhere in the same volume of the Political Register, however, are dozens of references to "the south," "the north," "southern," and "northern"—and in all of them, the words are lowercased (unless beginning a sentence or appearing in a headline). From this it follows that using the capitalized forms "the South," "the North," "Southern," and "Northern" may be anachronistic. I have seen many books that capitalize these terms anyway—presumably on the reasoning that today they would be capitalized, so why not retroactively?
I have mixed feelings about the capitalization of southern and northern. Historically "the south" and "the north" crystallized into "the South" and "the North"—and eventually the South tried to tear the Union apart. Ever afterward, "the South" and "the North" have remained the usual spellings for the two regions. Still, there is something hopeful and undetermined about referring to them "the south" and "the north" [of the United States] in connection with a time when civil war was not yet demonstrably inevitable. Ultimately, I think I would capitalize Southern and Northern in acknowledgment of the impending cataclysm, but it's a close (and subjective) call.
The Chicago Manual of Style, fifteenth edition (2003) offers a limited endorsement of uppercasing Southern and Northern in its list of examples of regional terms at 8.50:
the North, northern; Northern, Northerner (in American Civil War contexts); ...
the South, southern; Southern, Southerner (in American Civil War contexts); ...
Because Chicago comes out (at 8.2 of the fifteenth edition) four-square for what it calls "the 'down' style" ("the parsimonious use of capitals"), it may prefer southern and northern in any context not explicitly alluding to the American Civil War, but—as I noted earlier—I've seen many books that purport to follow Chicago and yet capitalize Southern and Northern in non–Civil War contexts.
Update (January 2, 2018): The guidelines in Chicago, sixteenth edition
After posting this answer, I acquired a copy of The Chicago Manual of Style, sixteenth edition, and can report that it retains the fifteenth edition's preferences with regard to southern/Southern and northern/Northern:
8.46 Regions of the world and national regions. Terms that denote regions of the world or of a particular country are often capitalized, as are a few of the adjectives and nouns derived from such terms. ...
[Relevant examples:] the North, northern, a northerner (of a country); the North, Northern, Northerner (in American Civil War contexts); ...
the South, southern, a southerner (of a country); the South, Southern, a Southerner (in American Civil War contexts); ...
The omission of "a" before "Northerner" in the list of examples appears to be an editing oversight or consistency error and not an indication that Chicago advocates saying "Johnny Rebel is a Southerner and Billy Yank is Northerner."
Elsewhere, the sixteenth edition endorses "the Union":
8.50 Political divisions—capitalization. Words denoting political divisions—from empire, republic, and state down to ward and precinct—are capitalized when they follow name and are used as an accepted part of the name. ... Used alone, they are usually lowercased.
[Relevant (but contrasting) examples:] the Ottoman Empire; the empire
the United States; the Republic; the Union
So the sixteenth edition considers "the Union" to be properly uppercased in the context of discussions of the United States. The parochialism of this view—which seems to grant special status to certain descriptive synonyms for the United States—is unmistakable; but I suppose that if we were to examine The Istanbul Manual of Style, we would probably find that it endorsed "the Ottoman Empire" and "the Empire" while relegating the U.S.-related entries to "the United States," "the republic," and "the union."