Clint was in medical for some reason and Natasha was playing "I'm packing my suitcase" with him to distract him. I think the scene starts when someone else (another avenger, maybe?) walks into the room? I remember them being in the middle of the game. Except googling for both "I'm packing my suitcase" and "I packed my suitcase" gave me nothing, so it might be another variation.
*I remember reading it on ao3.
*I think the reason he was in medical happened earlier in the fic.
*Natasha said she learned the game from an elementary school teacher.
*I am 99.9 percent certain it was NOT Clint/Natasha. If it was any pairing it was probably Clint/Coulson, since I think I was on a big Clint/Coulson kick at the time.