If I look at Boeing's site, a 737-600 comes with a CFMI CFM56-7 22,700 lb. End of story. No choices.
No doubt you can de-rate but that's not the point. Surely some parts of the World have real cheap crew so it would pay to have smaller engines flying at lower speeds to save fuel. Or someone else would like high density ops off short runways, and would like a pair of monster fans to pack the punters in?
These are not niche aircraft; they're made in their thousands.