On a wet afternoon here in England, having nothing better to do, I thought about East Coast Trot. I first heard this tune when the New Orleans cornet player Chris Tyle played it while on tour in England about 25 years ago, and I liked it immediately. I believe it dates from 1926 and was written by two gentlemen called Jimmy Blythe and Lathair Stephens. Probably it originally had lyrics, though I have never heard them.
In several years of hoping, I have not come across the printed music for this tune. Much of the tune's appeal lies in its melodic and structural simplicity because it lends itself very easily to improvisation. For a video of The Wabash Jazzmen playing it (in Eb), try this: https://www.youtube.com/watch?v=VlKwV7p_TDk