Depends on what type of tire you're running. If it's an old piecrust style slick, then 8" would be max. If you're going with something modern, then you can probably get by with a 255-60-15. A 7" is the minimum wheel size for that tire.
Steamer..... Haven't talked about tires for a LONG time. Anyone whose been doing this for awhile has seen it ALL... some good and some not good at all.
Going too much wider with the tire than the rim's width does start to make the sidewalls flare out. The wider the tire .... more the flare.
For some reason using a larger width rim (8, 10 or 12") are able to get away with a larger tire more so than 6 or 7 inch rims do. Also a wheel with a deeper off set also helps the larger tire with narrower rim combo work better.