In Southeastern Michigan, "Coney Island" refers to both a 24-hour diner, and, the specific kind of dry-chili-topped, grilled hot-dogs those diners serve. Here's a Flint-MI rendition of the chili. [LINK]
Pork shoulder has the double advantage of pairing well with both white and red wines, and being one of the cheaper cuts at the meat counter. Long-braised and roasted, it also delivers a huge amount of flavor. Serve these sandwiches with fresh cilantro sprigs and thinly sliced sweet onions (such as Maui) for each person to add to taste.