I'm not your cousin but from my experience, A simple "I'm sorry for your loss, thinking about you. Here for you if you need a shoulder to cry on or ear to listen." is all that should be said in the card. Going any more detailed could be stepping on a nerve that you didn't know even existed considering no couple deals with a miscarriage the same way. That's so sweet of you to do that for her. When I had my m/c I got a bunch of robotic "sorry for your loss" and only one person asked me for updates afterwards. Everyone left me in a hole to grieve for myself.
Your cousin definitely needs support atm but...if she asks for space or acts like she's ignoring you, don't take it personally. As previously said, everyone deals differently. If she needs her space she will come back around when she's comfortable.
