Cousin is a euphemism for
menstruation. Instead of saying "period",
girls often say "My cousin is here", or "My cousin has come", or sometimes "My cousin is visiting", to express the
idea "I'm on my period".
Amanda:
Girls, I can't hang out with you tonight. My cousin is here.
Sadie: Oh, sorry to hear that. You're having period
cramps agaian?
Amanda: Yep. They'are killing me righg now.