In scene 10 Stanley admits that he never believed Blanche's story about the oil millionaire, so why do you think he was playing along in the beginning of the scene?

Stanley was waiting for Blanche to bury herself.... to make a mistake.

STANLEY:
Was this before or after the telegram came from the Texas oil millionaire?
BLANCHE:
What telegram! No! No, after! As a matter of fact, the wire came just as--
STANLEY:
As a matter of fact there wasn't no wire at all!
BLANCHE:
Oh, oh!
STANLEY:
There isn't no millionaire! And Mitch didn't come back; with roses 'cause I know where he is--