The Titanic was a feature in country and rural black music (which, in truth, IS a type of country music) for quite a bit longer than it did in popular music.
Perhaps the best "country" Titanic song, is 1924's The Titanic (better known as "It Was Sad As The Great Ship Went Down") by Ernest Stoneman, who having recorded in every medium (except for CD) begining with Edison ca 1909 and ending with LP albums in the late 1960s/early 1970s can truly be said to have been the Father of Country Music.
Stoneman's 1924 performance was equalled, but not excelled, by the husband and wife team William and Versey Smith, black "street musicians" who released their own version of The Titanic in 1927. It is the same song, but totally different, and is as first rate a street-shouting performance as Stoneman's is excellent mountain country.
Titanic Blues, by Hi Henry Brown and Charlie Jordan, 1932, is a great twin-guitar number by a pair of St. Louis performers:
Some was drinkin'
some was playin' cards
some was in the corner praying to their God.
Loretta Lynn, in her autobiography, mentions a song about the Titanic she learned from her mother, ca. 1935-'40. In the film Coal Miner's Daughter, if you pay attention you can catch Sissy Spacek, as Loretta, singing a few lines of the soft, hymn-like song, which ends with the words "...will raise the Titanic some day." I've not heard that song anywhere else.
"Dolemite" the 1920s proto-rap about a black superhero, contains a Titanic section in which Dolemite finds himself aboard the sinking Titanic with women begging him to save them. He replies:
"I can paddle you back across the ocean with the end of my ____
I can eat nine pounds of cat s--- and not get sick."
Now, I GET the first line, but the significance of the second boast is has not stood the test of time. Every time I've used it as a pick-up line, my intended has been repulsed by it. But, I digress.....
Now, "Rabbit" Brown recorded a song called "The Titanic" in 1927. It is in no way related to the Stoneman/Smith song. This is a medicine show type of number, but backwards-looking in terms of 'feel' and with a few changes could have been written in 1875:
You know they all stood out on that sinking deck
and they was all in great despair.
Accidents may happen most any old time
and we know not when or where.