The rhyming title was a standby of early rock ‘n’ roll – “Tutti Frutti”, “Maybe Baby”, “Dizzy Miss Lizzie”, “Rock Around the Clock”, “Boney Moronie”, “Ooby Dooby”, etc. It seems harder to think of pre-rock ‘n’ roll titles that rhyme. I think the earliest I can come up with is “Come Josephine in My Flying Machine” (1910), which just beats “Roamin’ in the Gloamin’” (1911). Any other contenders?
Cheerful Little Earful (1930)
She’s a Latin from Manhattan (1935)
Semi-Rhyme: Shuffle off to Buffalo(1933)
I’m a Cranky Old Yank in a Clanky Old Tank on the Streets of Yokohama with My Honolulu Mama Doin’ Those Beat-o, Beat-o Flat-On-My-Seat-o, Hirohito Blues (1943)
There’s No Business Like Show Business (1946)
“Sally in Our Alley”, 1725
Jeepers Creepers, 1938
Seven Come Eleven (1939)
“It Don’t Mean a Thing if it Ain’t Got That Swing” one of the enduring jazz standards.
“I’m a Cranky Old Yank in a Clanky Old Tank on the Streets of Yokohama with My Honolulu Mama Doin’ Those Beat-o, Beat-o Flat-On-My-Seat-o, Hirohito Blues”
A Tisket a Tasket A Green and Yellow Basket
So, scanning the title of songs from this site from 1800 to 1923, I find only these songs with apparently purposeful internal rhymes, which makes the OPs hypothesis pretty spot-on. (Mind the overt, dated racism…)
1848: Wake Up Jake (No. 5 from SONGS OF THE SABLE HARMONISTS) [30 Dec] George Holman George Holman
1864: Abraham the Great and General Grant His Mate (Campaign Song for 1864) anonymous T. Brigham Bishop
1887: Razzle Dazzle Willard Thompson Willard Thompson
1897: Susanna, from Savannah (Negro Ditty) George Evans George Evans; arranged by Theodore Northrup
1899: My Susie-anna from Louisana (An Ethiopian Love Song) Tom McGrire Sid. L. Perrin
1910: Skid-dy-mer-rink-adink-aboomp (Means I Love You) (aka Skiddy-Mer-Rink-A-Doo) Felix A. Feist Al Piantadosi
1914: The Aba Daba Honeymoon Arthur Fields, 1888-1953 and Walter Donaldson, 1888-1964 Arthur Fields, 1888-1953 and Walter Donaldson, 1888-1964
1916: Arrah Go On, I’m Gonna Go Back to Oregon Joe Young, 1889-1939 and Sam M. Lewis, 1885-1959 Bert F. Grant
I’ve never seen the title as anything other than “A Tisket a Tasket”.
My Gal Sal (written by Paul Dresser, brother of Theodore Dreiser! I just found that out!)
True Blue Lou (as performed by Annette Hanshaw, Ethel Waters, et al.)
Weak internal rhyme but:
Mares eat oats and does eat oats.
Clearly alliteration was a bit more popular.
**O’Brien Is Tryin’ To Learn To Talk Hawaiian **(1917, recorded by Ada Jones)
That song’s just called “Mairzy Doats”.
I’m Looking Over A Four-Leaf Clover, 1933.
“Too-Ra-Loo-Ra-Loo-Ra” (“That’s an Irish Lullaby”) was written in 1914.
I’m sure that everybody here remembers **“Shoot the Sherbet to me Herbert”, **by Tommy Dorsey, ca. 1939 or earlier.
Well, along with “Roamin’ in the Gloamin’” from your OP, there’s Roamin’ to Wyomin’ (1924) …and Roamin’ in Wyoming (1940s)
I’m All Alone in a Palace of Stone (1926)
Mood to be Wooed (1945)
A Lane in Spain (1927)
“Sittin’ and Whittlin’” (a Hoagy Carmichael song I can’t find online)
Polly Wolly Doodle (1880)
Boogie Woogie Bugle Boy (1941)