For Iceberg Slim and his contemporaries, this was a jivespeak term for a type of con played on tricks who were looking for whores.

You can put a murphy on a square by giving him some dazzle about a freak dog in your stable that'll give him some fine circus love for just a few lines. Take him to an apartment building, and tell him that she's in a room on an upper floor, say room 1024. Tell him you'll collect the scratch here, then he can go meet her and have his fun. By the time he figures out that there's no one waiting for him in 1024, you'll be gone.

It's best to only pull murphys on tricks from out of town, otherwise it could hurt your reputation.