I have heard of that idea, bringing a scrapbook page for the bride... but I thought it was a bad idea for EXACTLY the reason you state.
I think it's kind of careless to ask people to do this without considering that many people will not have anything to contribute, leaving them stressed or wondering what to do, and ultimately, possibly embarrassing people who can't produce this requested page.
What you might do, if you don't have any pictures of you *with* your cousin, is do a page of your family, include some quotes or well wishes by each of you that are decoratively printed, or write up little cards with brief descriptions of memories you have of times spent with your cousin, and include those on a page with your picture. Another idea, if you or your mom are married, would be to do a page of your weddings, and include some nice wedding quotes or sayings, leave a spot for her to put her wedding photo next to yours, etc. You could do a food page, and decorate it with food items and some cutely printed recipes. Or make a page dedicated to her new last name... use decorative capital letters down the left side of the page, and write something lovely that corresponds with each letter, perhaps a wish for the new couple, or a piece of advice beginning with that letter, or a time you shared that begins with that letter...
With any of those ideas, you could embellish the pages as much as you like, without having to use a ton of pictures... hope this helps.