The "Coney Island Hot Dog" preparation did not originate with Coney Island, New York; the name merely refers to the origin of the hot dog itself, and also refers to the kind of restaurant that features them. The style originated in the early 20th century in Michigan, with competing claims from American and Lafayette Coney Islands (1917) in Detroit, and Todoroff's Original Coney Island (1914) in Jackson.
Competing, neighboring Coney restaurants in Detroit
Detroit style: In Detroit historically many Greek and Macedonian immigrants operated Coney islands, or restaurants serving Detroit Coney dogs. By 2012 many Albanians began operating them as well. The Greeks established Onassis Coney Island, which has closed. Greek immigrants established the Coney chains Kerby's Koney Island, Leo's Coney Island, and National Coney Island during the 1960s and early 1970s. All three chains sell some Greek food items with Coney dogs. National has most of its restaurants on the east side of the city, and Kerby's and Leo's have the bulk of their restaurants on the west side of the Detroit area.
Flint style is characterized by a dry hot dog topping made with a base of ground beef heart, which is ground to a consistency of fine-ground beef. Some assert that in order to be an "authentic" Flint coney, the hot dog must be a Koegel coney and the sauce by Angelo's, which opened in 1949. However, the sauce was originally developed by a Macedonian in 1919, Simion P. (Sam) Brayan, for his Flint's Original Coney Island restaurant. Brayan was the one who contracted with Koegel Meat Company to make the coney they still make today, also contracting with Abbott's Meat to make the sauce. Abbott's still makes Brayan's 1919 sauce available to restaurants through the Koegel Meat Company.
Jackson style uses a topping of ground beef, onions and spices. This referenced style is from Todoroffs Original Coney Island. However the Todoroffs' restaurants are now all closed and they only manufacture and distribute their coney sauce for retail purchase at supermarkets or other restaurants now. There are several other restaurants in the Jackson area that serve a similar but different type of coney, one of which is owned by an unrelated Todoroff family named Andy's Pizza. Andy's has 3 locations in the Jackson area. Along with this there are several other coney restaurants most notably being Jackson Coney Island and Virginia Coney Island. These are both located on East Michigan Avenue in front of the train station near where the original Todoroff's restaurant was located. These restaurants all use a blend of onion and spices similar to Todoroff's but instead use ground beef heart instead of ground beef for the coney sauce. Jackson takes their coneys very seriously. Each year Jackson Magazine or the Jackson Citizen Patriot have a best coney contest voted on by residents for all the restaurants in the area. 
Cincinnati's similar but distinct "Cheese Coney" is served with Cincinnati chili topped with grated cheddar cheese, mustard and a small amount of onion.