This thread has caused me to wonder whether any of the famous captains of industry/robber barons/moguls/business magnates/industrialists (choose your term) of the 19th century had any songs written about them.

Only 3 come to mind, and they're definitely satirical:
JAY GOULD'S DAUGHTER
SINCE HENRY FORD APOLOGIZED TO ME
MY NAME IS MORGAN (BUT IT AIN'T J. P.)
Anybody know of any others?

It could be that other songs exist(ed) but they've been forgotten.

It might be worth a search at places like The Library of Congress, The Levy Collection, Indiana University. I can't do it right now, but maybe later.

I found this list at Wikipedia of the kind of men I have in mind:

John Jacob Astor (real estate, fur) -- based in New York City
Jay Cooke (finance)-- based in Philadelphia, Pennsylvania
Daniel Drew (finance)-- based in the state of New York
James Buchanan Duke (tobacco) -- based near Durham, North Carolina
James Fisk (finance)-- based in the state of New York
Henry Flagler (railroads)-- based in New York City and Miami, Florida
Henry Ford (automobile)-- based in Dearborn, Michigan and the Detroit, Michigan metropolitan area.
Henry Clay Frick (steel)-- based in Pittsburgh, Pennsylvania and New York City
John Warne Gates (steel, oil) -- based in Chicago and Texas
Jay Gould (finance, railroads)-- based in the state of New York and New York City
Edward Henry Harriman (railroads)-- based in the state of New York
Collis P. Huntington (railroads)-- based in California, Virginia, and New York
James J. Hill (railroads)-- based in St. Paul, Minnesota
J. P. Morgan (banking)-- based in New York City. Presently JPMorgan Chase & Co.
John D. Rockefeller (oil, the Standard Oil company)-- based in New York City
Leland Stanford (railroads)-- based in Sacramento, California and San Francisco, California
Cornelius Vanderbilt (railroads, shipping)-- based in New York City

Let's add to that list:
Andrew Mellon
William Randolph Hearst