The Online 78 rpm Discographical Project lists 3 recordings of PUT ME IN YOUR POCKET:

Lee O'Daniel and the Lightcrust Doughboys, Vocalion 2731, 1933.
Bill Boyd and the Cowboy Ramblers, Bluebird 6670, 1936.
April Stevens, RCA 20-4381, ca1951.

The LP Discography lists it on one album:

Hank Locklin, "The Girls Get Prettier," RCA Victor LSP-3588, 1966.

And three 45-rpm singles:

Ferlin Husky (as Terry Preston), 4-Star 45-1542, ca1950.
Wilburn Brothers, 4-Star G-19, 1950.
Jeannie Pruett, MSR #1956, 1987.

Allmusic.com lists recordings by Elton Britt, Wilf Carter, Merle Haggard, Frank Ifield, and Mac Wiseman.