In the camping or grill supplies section of larger department or sporting goods stores, you should be able to find a flat grill basket intended for cooking hotdogs, burgers or fish. It should be very easy to mount the basket onto a rotisserie using hose clamps or even twisted wire, and a whole lot cheaper than buying a proper rotisserie basket.
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I've been thinking about this some and I have an idea or two, but I don't think this would work very well. The benefit of a rotisserie is that the meat is cooked all around but rotating over the heat. If you build a flat one then only one side is going to cook until you turn it over and then let the other side cook. I don't see the benefit of a flat rotisserie.