According to Craig I. Johnson's Jazz Pages, "My Canary Has Circles Under His Eyes" was written by (Music) Jack Golden, and (Words) Ted Koehler & Edward Pola, in 1931.

AMG lists it being sung by Debroy Summers on 2 anthologies:
"Silly Songs (1922 to 1934)," ABC CD #836169, 1992;
and "Mairzy Doats: 24 Great Comic Songs," Prism CD #137, 1997;
and by Eddie Erickson on "On Easy Street," Arbors CD #19111, 1996.