Based on such studies, I prefer to limit the quantity of red meat that my kids eat and substitute red meat with other sources of protein such as fish, poultry, and plant based protein. When I do serve my kids red meat, I prefer to select lean cuts of beef such as eye round steak.
You might think that lean beef is inevitably dry. However, you can serve up deliciously tender and moist lean beef by cooking it the right way. Stewing your meat in a liquid medium and cooking it low and slow by using a slow cooker, breaks down the protein and tenderizes the meat. My kids were especially fond of the soft consistency of the beef stew featured in the following video:
Pan A. et al. Red Meat Consumption and Mortality. Arch Intern Med. 2012;172(7):555-563.
Pollan, Michael. Cooked: A Natural History of Transformation. New York: Penguin Press. 2013.