"Roll Them Roly Boly Eyes" is the song that "started the decline of vaudeville," according to Joe Laurie Jr.'s 1953 book Vaudeville: From the Honky-Tonks to the Palace. This song is almost completely forgotten today but used to be very well known.
"Roly Boly" is sometimes spelled "Roley Boley" (as it is throughout Laurie's book), possibly because the actress May Boley was in the cast of the show. But the sheet music and other materials from the original run of the show spell it "Roly Boly." The song title of "Roll Them Roly Boly Eyes" varies from source to source too; It is variously listed as "Roll Them Roly Boly Eyes," "Roll Dem Roly Boly Eyes," and "Roll Those Roly Boly Eyes."
Cort's musical was written to showcase the talents of Eddie Leonard, a blackface minstrel performer who composed the song "Roly Boly Eyes" as well as the most famous song in the show, "Ida Sweet as Apple Cider," the latter of which predated the show. "Ida" has been recorded by Eddie Cantor (who also performed in blackface in his vaudeville days), Frank Sinatra, Bing Crosby, Bill Haley, and many other big-name artists.
Leonard's blackface act was considered old fashioned even in 1919, but he was so successful that he wore a diamond-studded belt that was adorned with real diamonds and looked after by a guard.
The video at the bottom of this article contains the only audio recording of Leonard I've found. In it, he sings "Ida" in dialect with frequent interjections of "wa-wa-wa" and "oh-oh-oh" and "doodly doo."
Leonard's oddball vocal style was frequently imitated by other performers. Al Schacht, the "Clown Prince of Baseball," did a vaudeville act with fellow baseball player Nick Altrock that is said to be the first act to feature "baseball clowning," and their grand finale was an impression of Leonard singing "Roly Boly Eyes." Billy Jones and Ernest Hare cut a record for Brunswick in 1922, "Eddie Leonard Blues," that references "Ida" and "Roly Boly Eyes" and imitates Leonard's vocal stylings. The California Ramblers recorded "Eddie Leonard Blues" for Vocalion. Ray Bolger (the scarecrow from The Wizard of Oz) did a brief impression of Leonard in this 1953 television performance. (The Leonard part begins at 2:06.) Bolger adds Leonard's trademark "wa-wa-wa."
Roly Boly Eyes was the apex of Leonard's career. Critics hailed it as one of his finest performances, and the songs lived on for decades. Leonard reprised "Roly Boly" and "Ida" in his starring role in the 1929 film Melody Lane, but the film was so poorly received that it ruined his prospects for a post-vaudeville life in Hollywood. Author Richard Barrios, in his book A Song in the Dark: The Birth of the Musical Film, described Melody Lane as "a fiasco, the first mammy picture to engender outright hostility from audiences as well as critics." Afterward, Leonard appeared in only one more film, playing himself (in blackface) in the 1940 Bing Crosby movie If I Had My Way.
Blackface minstrelsy endured, in a diminishing capacity, in Hollywood films until the early 1950s, particularly in the films of Al Jolson. In 1952, Teresa Brewer had a pop hit with a non-novelty remake of "Roll Them Roly Boly Eyes" that doesn't make any reference to Leonard's vocal mannerisms. By the time Brewer recorded her version of the song, things had come full circle; nostalgia for old songs and styles led to fads for honky-tonk piano albums and albums of "songs mom and dad used to sing."
I started reading about Leonard because I wanted to find out why Laurie called "Roll Them Roly Boly Eyes" the song that "started the decline of vaudeville," and I didn't find the answer. Very little has been written about Leonard. The Wikipedia article about him is unusually brief. Even Laurie, who mentions Leonard in passing a couple of times in his history of vaudeville, completely omits Leonard from the chapter on blackface performers. Leonard published a memoir in 1934, What a Life: I'm Telling You, that probably would be a good source of information, but it's long out of print and expensive to buy from rare-book dealers. I can speculate on why Laurie wrote what he wrote, though.
I'm guessing that Leonard was one of the last high-profile purveyors of old-style blackface minstrelsy and that his gimmicky performance of "Roll Them Roly Boly Eyes" was easy to imitate and mock. History, generally speaking, does not pay much respect to novelty songs. When Leonard's 1929 film Melody Lane flopped miserably, minstrelsy was already in decline, and Leonard—unlike Jolson—was strongly associated with vaudeville, not Hollywood. It's not hard to imagine that this goofy song, performed in a goofy way by a comical vaudeville performer with an antiquated style, could become a symbol of the decline of vaudeville. It's probably unfair of Laurie to say that "Roll Them Roly Boly Eyes" started the decline of vaudeville, but it was certainly a prominent emblem of vaudeville in its dying days.
An etymological note: "Roly boly" isn't a nonsense phrase. It comes from the Dutch word rollebol (roll + ball), which was absorbed into English as a name for a bowling-type ball game called "roly boly" or "roily bolly."