He did produce children, but not in the natural way. He synthesized them from peanuts. Few people recognized them as his progeny since they were not Black, but a sort of pale nutty brown.
Desirous of privacy, the one surviving son, Charles, adopted the surname Brown and eventually moved to Minneapolis, where he worked as a commercial artist. The rest, as they say, is history.
The gay rumor apparently originated from Carver’s idiosyncratic pronunciation of the word peanuts. One day a reporter visiting the lab overheard him exclaiming, “The more I know peanits, the more I love peanits! I just can’t get enough peanits.”