Looking further, I found something after all, an ARA ad in Billboard, October 27, 1945, page 25, announcing Phil Harris' "The Dark Town Poker Club" and "Jellybean" on ARA 116 and The Town Criers on ARA 126 as "2 New Releases".
Apparently ARA had delayed the release of this one here because of the sales success of Phil Harris' "That's What I Like About The South" on RM 104.
Xiphophilos, thanks for editing several ARA records yesterday. I had to remove the release month of March for this one though because, against my yesterday's comment on RM 104, the ARA ad in Billboard March 31, 1945 did not list all numbers from 101 to 118 and 3001 and 4001. In fact, numbers 113, 115 and 116 (this one here) were missing.
They were not listed in the updated ARA ad in Billboard, May 26 1945 page 26 either, so a later than May 1945 release of this one here is implied.
As said before, I cannot verify a more specific release date of June 1945, so I have changed it back to just 1945.
Made "alt. label" the main images because it seems clear now that this label design, with the label name "American Recording Artists" written out on the rim, came first.
Looking further, I found out that we had this record twice on the database (once under Phil Harris and once under Phil Harris & Orchestra). I have merged them to this entry here which already had the correct data and excellent images, too.
The title of side B is Jelly Bean, not Jelly Bran. The composers of Jelly Bean are Rosen-Vergis-Dupre, Sam, Joe and Jimmy respectively. Vodery was involved with the Darktown Poker club, but not the flip side.
"The Dark Town Poker Club" was co-written and originally performed by Bert Williams, "by far the best-selling black recording artist before 1920" according to Wikipedia. It seems that this one, Harris' original version of it, was recorded in 1945, so the proposed 1944 date could not be right, but also the current 1946 is probably not correct (although this record charted various times in 1946 and 1947, along with Harris' re-recording for RCA Victor).
See Lost Sounds: Blacks and the Birth of the Recording Industry, 1890-1919 by Tim Brooks, p. 146:
"In 1945 Harris recorded 'The Dark Town Poker Club' for the small ARA label of Los Angeles, rerecording it for Victor when he joined that label in 1946. Both versions were substantial sellers, placing on the Billboard charts in 1946 and 1947 ..."
I once found a more specific release date of June 1945 but can't verify it for now, so I'll change it for just 1945.