"...Welcome to our mine, Yeah. Welcome to our toil. Welcome to our trouble, 'Neath the earth and soil. You'll sweat a little water, And you'll sweat a little blood, And you might get out if the mine don't flood..."
Though one person adds: "I swear they used to say 'welcome to the bowels, beneath the earth and soil'"
Initial searching makes it look like it's also been used at Dollywood for their former ride "Flooded Mine"
Interestingly, there's an article about your theme park bearing the name of this song (“Sweat a little water, sweat a little blood”: A spectacle of convict labor at an American amusement park by Patricia Morris and Tammi Arford) but unfortunately it doesn't focus on the origins of the song.
I couldn't find any lines of the song in historical newspapers or books on Archive.org, so my assumption is that it's a modern creation, but no firm evidence to back that up.