Surely the Lufthansa 737-100s, the first built, had a Flight Engineers console. There are several references to this but I can't find a photo.
Just 30 series 100's were built, with 22 going to Lufthansa, 5 for Malaysia (Singapore) Airlines and 2 for Avianca.
Interesting. I often flew on the flight deck of MSA's 737s. I thought they were 200s - but they had only two crew. I'm sure there was never a Flight Engineer's console on any 737.
PS. ChitterneFlyer, disregard Krakaprat.