Captain America & Black Widow Have a SON in The Comics
Captain America and Black Widow officially have a son - or, at least, they do in one alternate future timeline. Marvel Comics has always enjoyed exploring the Multiverse, using the concept as the key to exploring countless different "What If?" timelines.
One of the most enjoyable was created by Greg Johnson, Craig Kyle, and Christopher Yost in the excellent animated movie Next Avengers: Heroes of Tomorrow. This was a stunning animated epic set in a future timeline where he next generation of Earth's Mightiest Heroes assembled to save the world. They were a fun team, and it didn't take them long to become part of the Marvel Comics Multiverse as well.
Writer Brian Bendis brought the Next Avengers into comic book continuity in an epic time travel adventure that saw the entire timestream break down. Kang the Conqueror recruited the Avengers of the present to save the timestream, and they traveled to a dystopian future world ravaged by the forces of Ultron, where they were charged with rewriting history so as to preserve the timestream. The Avengers never truly processed the reality of who they were dealing with - probably a good job given almost all the Next Avengers are directly related to them. James Rogers, for example, is the son of Captain America and Black Widow. He has similar superhuman abilities to both his parents, including all the benefits of the super-soldier serum and likely the delayed aging of Black Widow; in honor of his father, he wields a sophisticated energy shield to devastating effect.
On the face of it, Natasha Romanoff and Steve Rogers should be complete opposites; one is a straight talker who believes in honor and loyalty, the other is Marvel's premiere super-spy. But, as the old adage says, opposites sometimes do attract. For all that's the case, though, there is some evidence James Rogers may have actually been artificially created by some sort of genetic experimentation, rather than conceived through natural means. Natasha was actually sterilized when she was just a child, meaning she shouldn't be able to have a child in any timeline.
Curiously enough, there's never really been a romantic relationship between Black Widow and Steve Rogers in the comics - but one of Natasha's main romances is actually with Bucky Barnes, who became Steve's successor as Captain America. The MCU hasn't really developed that idea, instead opting for an unexpected romance between Black Widow and the Hulk in Avengers: Age of Ultron, but a lot of viewers felt Scarlett Johansson's Black Widow and Steve Rogers' Captain America had quite the chemistry in Captain America: The Winter Soldier. Who knows - with the MCU embracing the Multiverse in the upcoming What If..? series, perhaps that could yet be developed.