Are you close with your cousin? Just ask about it.
Or find out who the caterer is, and ask them if they typically bring a few "emergency" vegetarian dishes to weddings. I've heard of caterers who do. My roommate went to a wedding as a "plus one" recently, too late to even request a meal option. When the caterers asked what meal she'd chosen she said she hadn't, and that she was a vegetarian. They said no trouble, they always had enough food to make a few vegetarian meals. Caterers see this all the time, especially when brides make menu choices that don't include a vegetarian option!
If your cousin is a horrific person, you don't want to call, the caterer tells you to eat **** and die (or any other very remote possibility...) Just write on the card, "I'm a vegetarian. So, nothing, it seems." Or, you know, your less snarky option of "I'm a vegetarian. So, any vegetarian side dishes."
Worst case scenario? Eat before the wedding, and don't eat at the reception. I've not eaten for 14 days. You'll survive a few hours, I promise!