James Madison, not a Christian, but a "Theistic Rationalist":

A while back I did a post on Madison where I noted that like Washington, he often spoke of a warm-intervening God, generically defined, but eschewed talking in Christian or Trinitarian terms, and otherwise was mum on the specific details of his creed. I linked to an excellent article by James H. Hutson on Madison's religious beliefs which noted our fourth President's conspicuous silence on the matter. Hutson does uncover a few clues as to what Madison believed. And those clues point us in the direction of Madison's belief not in Christianity, but in Theistic Rationalism. First, the words of Bishop Meade, a Founding era orthodox Christian who knew Madison personally:

His religious feeling, however, seems to have been short-lived. His political associations were[with] those of infidel principles, of whom there were many in his day, if they did not actually change his creed, yet subjected him to a[the] general suspicion of it

Note: the bracketed words are from an alternate citation of this quotation offered by David L. Holmes in his book, The Faiths of the Founding Fathers. Replace "with" for "were" and "the" for "a."

Meade also noted:

I was never at Mr. Madison's but once, and then our conversation took such a turn--though not designed on my part--as to call forth some expressions and arguments which left the impression on my mind that his creed was not strictly regulated by the Bible.

Hutson's paper also notes a Bostonian's account of an 1815 dinner conversation with Madison:

He talked of religious sects and parties and was curious to know how the cause of liberal Christianity stood with us, and if the Athanasian creed was well received by our Episcopalians. He pretty distinctly intimated to me his own regard for the Unitarian doctrines.

Clues, yes. But nothing from the horse's [Madison's] mouth. Although, in an era when orthodox Christianity was far more socially and legally entrenched and when one could ruin one's reputation by wearing one's heterodoxy on one's sleeve (what happened to Paine), keeping "religious secrets" as Madison and Washington did, seems to me to point strongly in the direction of adhering to the so called "infidel principles," commonly believed by the elite Whigs of the Founding era.

But I have uncovered an interesting letter from Madison, written in 1825, which I think sheds some light on Madison's personal beliefs. I'm going to reprint the entire letter TO FREDERICK BEASLEY on Nov. 20, 1825, which you may also read here.

I have duly recd the copy of your little tract on the proofs of the Being & Attributes of God. To do full justice to it, would require not only a more critical attention than I have been able to bestow on it, but a resort to the celebrated work of Dr. Clarke, which I read fifty years ago only, and to that of Dr. Waterland also which I never read.

The reasoning that could satisfy such a mind as that of Clarke, ought certainly not to be slighted in the discussion. And the belief in a God All Powerful wise & good, is so essential to the moral order of the World & to the happiness of man, that arguments which enforce it cannot be drawn from too many sources nor adapted with too much solicitude to the different characters & capacities to be impressed with it.

But whatever effect may be produced on some minds by the more abstract train of ideas which you so strongly support, it will probably always be found that the course of reasoning from the effect to the cause, "from Nature to Nature's God," Will be the more universal & more persuasive application.

The finiteness of the human understanding betrays itself on all subjects, but more especially when it contemplates such as involve infinity. What may safely be said seems to be, that the infinity of time & space forces itself on our conception, a limitation of either being inconceivable; that the mind prefers at once the idea of a self-existing cause to that of an infinite series of cause & effect, which augments, instead of avoiding the difficulty; and that it finds more facility in assenting to the self-existence of an invisible cause possessing infinite power, wisdom & goodness, than to the self-existence of the universe, visibly destitute of those attributes, and which may be the effect of them. In this comparative facility of conception & belief, all philosophical Reasoning on the subject must perhaps terminate. But that I may not get farther beyond my depth, and without the resources which bear you up in fathoming efforts, I hasten to thank you for the favour which has made me your debtor, and to assure you of my esteem & my respectful regards.

Letter from James Madison to Frederick Beasley (Nov. 20, 1825), in 9 The Papers of James Madison, 1819-1836, at 229 (Gaillard Hunt ed., 1910).

While Madison is not entirely explicit regarding what he really believes, there are two important clues which point in the direction of Madison's personal disbelief in orthodox Christianity, instead belief in the same system of Theistic Rationalism in which Jefferson, Adams, and Franklin believed. First, when it comes time to discuss God's attributes, Madison does not, which it would seem he would do were he a Christian, turn to the Bible or the explicit creeds of the Episcopal Church to which he nominally belonged, but rather, he attemps to understand God's attributes on rationalistic terms, through philosophical reasoning.

Second, the "Dr. Clarke" to whom Madison refers is "Dr. Samuel Clarke," an Anglican minister, also a theological unitarian who was nearly defrocked for peddling his unitarian doctrines (he wasn't defrocked because he promised to stop doing so). Indeed, in Gregg Frazer's Ph.D. thesis, he notes that Clarke's work was part of what the orthodox Christians of the day referred to as "Satan's bookshelf" at Harvard, an institution which had orthodox Christian origins but during the Founding era was overtaken by Unitarians.