So it'll be a hitch-mount for you. As for the rack, you have several good choices. Yakima, of course, always makes reliable stuff; their BackSwing 4 ($350; www.yakima.com) accommodates a wide variety of bikes, is very secure and easy to use, and swings away from the rear of the vehicle when you want to get out the Coleman cooler. Yakima's Bighorn ($170) holds four bikes more economically, but lacks the swing-out feature, which is of course extremely useful when traveling with a crew. Thule's Trailblazer ($399; www.thuleracks.com) is similar in capacity and features to the BackSwing; maybe a little more ruggedly built.
But what to do about the Diamondback? Get a "top tube adapter," which creates a top tube for clamp mounts. They run about $25; Yakima makes one, and so does Softride (www.softride.com).
You might also look at the SportsWork TranSport, a tray-type hitch rack that is rugged and highly regarded. It's $300 in the two-bike configuration, but trays for a third and fourth bike can be added if you have a two-inch receiver on the Expedition, which I expect you do. Setting up the TranSport for four bikes will run about $450 (www.bicycleracks.com).
For more sport-rack reviews, check out Outside's 2004 Buyer's Guide.