Marvel's Spider-Man, despite his constant irresponsibility and struggle to balance his life, has a reputation for having many relationships in the Marvel Universe. Peter Parker has dated Gwen Stacy, Mary Jane (whom he even married), Black Cat and multiple other people throughout his tenure as a superhero. It isn't surprising, then, that Marvel once attempted to pair him up with Captain Marvel - but this short-lived attempt in the comics would unfortunately never work in the Marvel Cinematic Universe.
Peter Parker's dating life is complicated; it is infamous for being one of the major components of his 'normal' life he regularly abandons or neglects whenever he needs to swing into action as Spider-Man. This leads to Gwen Stacy mistrusting him, Mary Jane to look for partners elsewhere, and only certain superheroes like Silk and Black Cat understanding his priorities - but still feeling neglected whenever Peter fails to properly multitask. But for a short time, Marvel editorial decided to pair him up with Captain Marvel, who is decidedly more mature and adult than the other people whom Spider-Man has dated. Unfortunately, it was not to last.
In Ms. Marvel #34, written by Brian Reed with art by Paulo Siqueira and Adriana da Silva Melo, Spider-Man interferes with Carol Danvers' missions. Carol, who was going by the name Ms. Marvel at the time and stripped of her powers, fights with both her enemies and Spider-Man, who - true to form - quips during the entire fight. He also spontaneously asks Carol on a date if he helps her, much to her surprise (and his own). Captain Marvel, perhaps in a bid to succeed in the mission faster, accepts.
In Ms. Marvel #47, the two actually go out to an expensive restaurant (Carol buys dinner), and make fairly pleasant if slightly awkward conversation. The date is interrupted by soldiers bursting through the window and attacking Carol, but with her powers restored, she makes short work of them. Marvel would tease a future relationship in multiple issues after but never seriously pursue it again; Captain Marvel would go on to date James Rhodes (War Machine), and Spider-Man would get back together with Mary Jane (in a manner of speaking; the resumed their on-again, off-again romance).
Thanks to the age difference between Spider-Man and Captain Marvel in the MCU, this relationship will most likely never be seen on the big screen. The same is true for Carol's relationship with War Machine; Captain Marvel actor Brie Larson is in her 30s while War Machine actor Don Cheadle is almost 60 years old. Captain Marvel and Spider-Man are well-written characters who work well together, but perhaps it's for the best that their relationship never moved beyond one date.