I'm not a big fan of team fic where they all move into Stark Tower unless it's crack fic. I don't see why a group of adults who hardly know each other would be willing to do that.

Heh, I'm probably alone in that I don't think either Clint or Natasha has a big connection to Coulson. :P Clint likes Coulson because he thinks Coulson is a good commanding officer, but that's the only connection they have (because I didn't get a vibe beyond 'commanding officer and snarky field agent' in Thor). In my headcanon Clint has a strike team who he's been working with for years and they go for beers after work, but he doesn't have what could be considered close friends.

As for Natasha, I think she and Maria are friends. Maria is up front with people to the point of being blunt, and I think Natasha would find that refreshing in a world of spies. As for Coulson, I once wrote in a fic that "Natasha couldn't bring herself to trust someone who offered sweets with one hand and issued kill orders with the other," and that's my headcanon for them.

I'll have to think more about my headcanon for how Clint and Natasha would get along with the other Avengers.