I have been living in apartments all my life and none would allow me to rent a one bedroom because I had a male child. Where I'n living at now, I notice that they are renting one bedrooms to entire families. I even had a young couple upstairs with an overactive son of whom I had to listen while the two adults were having sex and the young boy banged on the bedroom door.
There are local regulations regarding the number of occupants for an apartment. However, there is no rule against renting a one bedroom apartment to a man and woman. That being said, a landlord can rent or not rent to whomever they wish as long as they are not discriminating against someone based upon ethnicity, race, gender, etc.