From Ann's books it looks like they recorded 36 under the name Riverside Ramblers. I don't know of a complete collection but there is this:
Arhoolie at http://www.arhoolie.com/titles/7050.shtml
Out of that selection, these are by the Riverside Ramblers:
One Sweet Letter
One Step de L'Amour
Fais Pas Ca
Darbone's Creole Stomp
Mon Couer Ma Fais Ci Mal
There's a compilation called Gran Prairie: A Cajun Music Anthology: The Historic Victor/Bluebird Sessions 1935-1940 that has La Valse de la Prison and Breakdown a Pete on it.
I have Valse de Vieux Temps from a 78.
Un Piastre Ici, Un Piastre La Bas is credited to Riverside Ramblers.
I know I have heard the following on compliations here or there but I can't remember just where (maybe JSP or Proper box sets?:
Shreve Breakdown
Josephine, My Josephine
One Step de L'Amour
It's a shame they're hard to find in one place!
I was very fortunate to see them 30 years ago at one of the early Festivals Acadiens. The Hackberry Ramblers that day were Luderin Darbone on fiddle, Edwin Duhon on guitar, Roy Morgan on guitar and most of the vocals, and Crawford Vincent on drums and washboard. They were in "uniform," all dressed in white short sleeve shirts and ties and black pants. They were in their early 60s at that time and still in great shape and great voice. I regret I never got to hear Lennis Sonnier live.
Bluebird (label)
8000 A Right Or Wrong
8000 B One Sweet Letter
Montgomery Ward (label)
7338 A Dissatisfied
7338 B Wondering
7339 A Drifting Along
7339 B Stay In Your Own Backyard
7340 A Louisiana Sweetheart
7340 B Old Fiddle Blues
7341 A I Ain't Satisfied
7341 B Ain't Gonna Give You None
7672 A Little Acadian Girl
7672 B There'll Come A Time
7673 A Was It Tears
7673 B Longing For You
7674 A Let's Go Fishing
7674 B She's One Of Those
7675 A Right Or Wrong
7675 B One Sweet Letter