From The Journal of the Brotherhood of Boiler Makers and Iron Ship Builders of America, Vol. 15, No. 8 (Kansas City, Kas., Aug. 1, 1903), page 407:

Brother Lasarus Bloomberg made a hit in a number of popular songs and Bro. Buck Murphy brought tears to the eyes of some of the boys by his creditable rendition of that sentimental song, "Only a sliver from my sweet-heart's wooden leg." Brother Tommy Ward rendered a very catchy song entitled, "We had to move Paddy's grave to dig a sewer." Brothers Jurgenson and James L. McGuire of Lodge No. 385 San Francisco who were guests of the evening kept the boys laughing by singing all the popular coon songs....

I found similar references to:

"They Are Moving Willie's Grave to Build a Sewer" 1907

"They Are Moving Willie Brennan's Grave to Dig a Sewer" 1908

"Why Did They Move Poor Willie's Grave to Build a Sewer?" 1908

"They Are Shifting Mother's Grave to Build a Sewer" 1908

"They Are Moving Father's Grave to Dig a Sewer" 1913

"They Moved Father's Grave to Build a Sewer" 1918

In each case, only the title was mentioned.

Then I found no further reference to similar titles until 1961!