Richard Diamond, Private Detective
Richard Diamond has it all. A former NYPD cop turned private detective, he has biting sarcasm, a Park Avenue millionaress for a girlfriend and even concludes each episode with a song!
Starring Dick Powell, Diamond is definitely light-hearted detective fare that keeps you smiling even through the murders, kidnappings, and other standard detective-genre crimes.
Here is a sample of the online episodes currently available at The Old Time Radio Fan:

Tom Waxman, Union Leader Killed by Bomb
1949-06-26 (13.25 MB) [28:57]
Mrs. William Baker, Klepto
1949-09-03 (12.99 MB) [28:22]
Neighbor Tries to Ruin Diamond's Voice
1949-11-05 (13.08 MB) [28:34]

Sidewalk Photographer Card and Negative
1950-03-26 (13.47 MB) [29:25]

Death, Package Statue of Kali William Logan
1950-04-05 (12.87 MB) [28:07]
Edna Wolfe Case
1950-08-09 (6.83 MB) [29:51]

Wheat Germ Juice Bar Case Ice Pick Murder
1953-08-09 (13.85 MB) [30:15]

Hat Pin Case Will Baxter Oklahoma Cowboy
1953-08-16 (13.67 MB) [29:52]