Should be noted that "FDR's Back Again" is, after all, a Cox remake of the Bob Miller song, "Those Good Old Times Are Coming Back Again" (1932). This was recorded by Miller for Columbia and ARC, by Ernest Hare on Velvetone (as "Hobo" Jack Turner) and on Columbia (as Earl Harris), and by Bill Elliott (as Jim Baird) on Victor. The Elliott recording is available on one of the Yazoo "Hard Times Come Again No More" compilations of depression songs and is probably the most interesting, as it's accompanied by an organ that sounds like it escaped from a skating rink. Miller's own version can be found at jazz-on-line.com, credited to "Bob Miller's Orchestra." (This version features clarinet, trumpet, et al and was released in the Columbia popular music series; Bob's ARC recording was done with hillbilly instrumentation.)

Some of Cox's lyrics are anticipated in the Miller song, but oddly Miller wrote it all in one strain. Cox added a chorus part, which improves it quite a bit (IMO, of course). Miller's original is a counterpart to (and probably an imitation of) "Happy Days Are Here Again," with some not overly specific assertions that life is getting better and the end of the Depression is in sight.

Lyrics from the Miller version, Columbia 2644-D:

Oh, them good old times are coming back again (x2)
And the good old sun will shine
And there won't be no bread line
Oh, them good old times are coming back again.

Yes sir, them good old times are coming back again
Oh, them good old times are coming back again
We won't have to break our backs
Toting a big carload of tax
Oh, them good old times are coming back again.

Yes, them good old times are coming back again
Oh, them good old times are coming back again
And the long-eared mule will say
To the elephant that day
Them good old times are coming back again.

Yes, sir, I'm saying them good old times are coming back again
I mean, them good old times are coming back again
We'll have money in our jeans
And we'll eat more than turnip beans
Oh, them good old times are coming back again.

Cox was undoubtedly acquainted with Miller, as he recorded Bob's "Trial of Bruno Richard Hauptmann." Ballad Index lists Miller as the probable composer of "Fate of Will Rogers and Wiley Post," which Cox also recorded for ARC in the mid-1930s, which seems probable to me as well. At any rate, "FDR" is an offshoot of "Good Old Times," though by most objective standards it's superior to its inspiration.