While much has been made of Captain Marvel's potential love interests in her MCU franchise, it rarely has been pointed out that she already has a frequent romantic partner in the comics: James "Rhodey" Rhodes aka War Machine. This might seem a bit random at first, but the two have quite a lot more in common than first appears.
Carol Danvers first appeared in Marvel Super-Heroes #13 in 1968, while James "Rhodey" Rhodes first appeared in Iron Man #118. Both characters came from a military background, with Rhodey a helicopter pilot in Vietnam (though this was later updated) and Carol a United States Air Force security chief. Both characters were also first established as supporting characters to a main protagonist. For Carol, it's the Kree hero Captain Marvel - whose mantle she will one day assume, and for Rhodes, it's Tony Stark, who will eventually design the War Machine armor Rhodes will be best known for. Rhodes became a consistent mainstay in the comics, even taking over for Tony Stark as the latter descended further into alcoholism during The Demon in the Bottle storyline. Carol received her own series as Ms. Marvel in 1977 and gradually became one of Marvel's most visible female superheroes.
Carol and James' relationship is a newer addition to the comic continuity. To some degree, this makes sense, as, despite their similarities, the characters didn't actually share that much page-time in the comic books until relatively recently. However, the reasoning behind the relationship was pretty clear, with their romance largely fitting into the lead-up to Civil War II. During the comic book dust-up, Rhodes is mortally wounded in a battle with Thanos, driving a wedge between Rhodes' best friend Tony Stark - and his lover Carol Danvers. The conflict would eventually escalate until both characters were leading opposing factions of the superhero community, culminating with Carol putting Tony Stark into a coma (which apparently lead to his demise). Rhodes didn't stay dead, however, and as of Captain Marvel #5, the two have seemingly resumed their relationship with a kiss.
Whether an on-screen version of this relationship will show up in the MCU is anyone's guess. Many fans have pointed out the considerable age gap between the actors - Don Cheadle, who plays James Rhodes, is 55, compared to Captain Marvel's Brie Larson, who is 30. There is also quite a lot of alternative pairings suggested by both fans and lore. Whatever happens in the MCU, however, it seems Carol Danvers and James Rhodes (Jarol? Danvodes?) are a couple yet again - apparently all is fair in love and war machines.