One thing that would probably really help her is to be given some easy, healthy recipes that she can make herself. Here are a few sites with DELICOUS healthy recipes to try out (I'd give you specific recipes, but I don't know what kinds of foods your cousin likes).
(My favorites are the PF Chang's style Thai lettuce wraps and the Panera knock-off Asian chicken salad. Actually, all of the entree salads are really good).
(Most of the recipes only have information about Weight Watcher's Points Plus, but you can figure out the rough calories since 1 PP (point plus) equals about 40 calories).
One thing to remind your cousin of is that she probably shouldn't make any foods absolutely "forbidden"; she can still eat treats as long as they're reasonable portions, and not every-day occurrences. No, no one needs red meat, but eaten occasionally, cooked healthily, and as part of a larger healthy diet, I think it's just fine. Turkey can make a good substitute for beef in many recipes though, if she does want to cut down on red meat.
Also, a few food that have really helped me find lower-calorie alternatives to what I was eating are jello pudding cups (much lower calorie than a candy bar), laughing cow and babybel cheese (both are great eaten with fruit such as an apple or some grapes as a snack), greek yogurt (can be used as a healthy substitute to mayonnaise or cream in recipes), honey as a sweetener (instead of white sugar) and brown rice (instead of white).
Also maybe encourage your niece to start lifting weights. In my experience, it's a wonderful way to feel better about your body, and the impact it has on your figure can be seen within just a few weeks of starting. If you like to work out, offer to take her to the gym - exercise is both more fun and easier to stick to if you have a partner/friend/relative there with you.
Best of luck to you and your niece! She's so lucky to have an uncle like you to look up to!