Attendees do not normally give gifts. Your attendance is the gift. Physical gifts are normally given departure or retirement ceremonies. Always touching, they are usually also humorous.
However, you being a civilian family member, something meaningful and discreetly given is not only appropriate but will be treasured.
Should you decide to do this, a challenge coin or service tie would do nicely. Selection should be limited to something you can legitimately give and your cousin and legitimately use (don't give her a Navy tie). You can get some ideas from this website; www.medalsofamerica.com.
As far as meaning, you actually already know that. The gift would represent something important in your cousin's life or career. Maybe even something shared with you.
My recommendation, consider a challenge coin. If you find one you think right, is given discreetly through a handshake. And it is never forgotten.
So, tattoo your family tree on her butt.
LOL. Sorry, old sailor humor.