You need to wean them off the meat, see. Make the meat portion smaller, or in more pieces. Example: Beef Stew. Then, proceed to make the meat less important. Example: Spaghetti with some-meat-and-sauce. Make the meat less important in the meal. Example: Stir Fry Beef with Bell Peppers (lots of peppers, very little beef). Work toward things like "Ham and Bean Soup" or "Beef Vegetable Soup". There should be more bean than ham, more vegetable than beef. Tout it as healthy. Pitch it as a cost-savings measure (a large portion of why I don't eat meat is that it's too damn expensive for what you get). Say it's for cholesterol levels. It doesn't really matter what rationalization you use. Just, y'know, less meat.

Eventually they'll think that peppers and garlic over sketti is a great meal. It's all a matter of acclimating. :)