To my knowledge, only two airlines used 3-man crews on the 737, during its introductory years: United, and Western. I've been told the third guy really didn't even have any real duties (ie, there was no "Engineer's Panel"); merely an ALPA-appointed position to preserve pilot numbers.

Delta was a late-comer to the 737 too; they might not have flown them until they bought Western. (Can't remember).

I don't think the third-man lasted much more than a year or so.