I'm a little late to the party, but I went and looked and I have 160+ bookmarks tagged MCU on my pinboard. Some of those are Clint/Natasha, but I've got all kinds of other pairings (and gen.) Some of them go back to the first Iron Man movie, so canon varies, but they're all things I've loved.

To start off:

All MCU (https://pinboard.in/u:topaz119/t:fandom:MCU/) (all pairings: slash, het, gen, rpf)
Tony/Pepper (https://pinboard.in/u:topaz119/t:pairing:Tony%252fPepper/)
Darcy/Clint (https://pinboard.in/u:topaz119/t:pairing:Darcy%252fClint/)
Bruce/Natasha (https://pinboard.in/u:topaz119/t:pairing:Bruce%252fNatasha/)
gen (https://pinboard.in/u:topaz119/t:category:gen/t:fandom:MCU/) (there might be a pairing but it's not the focus of the story)

I could keep slicing and dicing, but you get the idea. At a minimum, I tag with fandoms and pairings; ratings are in the description. I only occasionally mention warnings, so you might want to check those on the fic itself. Some of the bookmarks in the Iron Man or Captain America tag are comics-verse, but I think I've managed to get them all tagged with some variation of 616. (There's also a Hawkeye tag (for the comic, not the character) that might be of interest around these parts.)

Enjoy (and please feel free to ping me with any questions!)