So, you can use Max's magic multi site tool to search for "Darby's Ram," and as far as I searched I couldn't find any version with lyrics matching Grandpa Jones'. It's interesting to see how many version of this song there are. This site attributes the song to "A. Delmore / Louis Jones."
Darby's Ram (A. Delmore / Louis Jones)
Ol' Darby lived across the creek, and when 'e told a tale Ev'ry minner in that creek was big as Jonah's whale My daddy had an ol' buck sheep, and then you'd hear him say One of the finest rams, sir, that ever fed on hay Well 'e had four feet to walk, sir, and 'e had four feet to stand Ev'ry foot he had, sir, would cover an acre of land
Oh, wa'n't he a big one, boys Wa'n't he a big one, boys Wa'n't he a big one, boys Before they cut 'im down
Now the wool that growed on that ram's side reached to the ground And it sold to Mistah Johnson for fourteen hundred pound The wool that growed on that ram's back reached up to the sky The eagles built their nest there for I heard their young ones' cry
Oh, wa'n't he a big one, boys Wa'n't he a big one, boys Wa'n't he a big one, boys Before they cut 'im down
Now this ol' ram, he had a horn, an' it reached up to the moon A man went up in January and he never got back 'til June Now the butcher man that cut him down was washed away in the blood And the little boy that held the bowl went drownin' the flood
Oh, wa'n't he a big one, boys Wa'n't he a big one, boys Wa'n't he a big one, boys Before they cut 'im down