Welllllllllllll, you can always put them in a scrapbook. You could get a 12x12 scrapbook so the pages are big enough for the larger cards. If you get the kind with drop in sleeves, you can put the cards on a piece of decorative 12x12 paper then slide them into their protective sleeve so everyone can see them and you could get 3 or 4 on a page, maybe write a little bit about the Yorkie or member under the card if you've come to know them. That's my obvious answer since I am an avid scrapbooker.
ETA: Most scrapbooks are expandable, so you can continue to add years as you go along.