Your second song is considerably older, also known as 'The Dying Cowboy' (several with that title though) sometimes ascribed to N. H. Thorp, but more probably H. Clemons of Deadwood, S. Dakota in 1872. In turn this was based on a song called 'The Ocean Burial' by Capt. Wm H Saunders tune by Ossian Euclid Dodge in the 1850s.