Okay, here's the link I was looking for, and some older detective stories from it that are supposed to be funny private eyes...
The mini-list is excerpted from
www.thrillingdetective.com/trivia/humour.html
(I only listed the old stuff in hopes they were public domain by now. Not sure where the general cutoff is. Is the date of the author's death that starts things, or the date of the book?)
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Bill Crane Created by Jonathan Latimer:
* Headed for a Hearse (1935; AKA. The Westland Case)
* The Lady in the Morgue (1935)
* Murder in the Madhouse (1935)
* The Dead Don't Care (Doubleday, 1938)
* Red Gardenias (1939; AKA Some Dames Are Deadly)
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Max Latin Created by Norbert Davis (1909-49):
SHORT STORIES
* "Watch Me Kill You" (July 1941, Dime Detective)
* "Don't Give Your Right Name" (December 1941, Dime Detective: also The Hardboiled Dicks)
* "Give the Devil His Due" (May 1942, Dime Detective)
* "You Can Die Every Day" (December 1942, Dime Detective)
* "Charity Begins at Homicide" (October 1943, Dime Detective)