Best bet would be to check with your local building dept., but I would think 2"x6" @ 16" o.c. would be sufficient for 1/2" regular. Is this going to be an enclosed porch? If it's just going to be screened, I'd highly recommend using wood rather than drywall....
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right now is it open up to the rafters, or will you be hanging another ceiling off the existing ceiling?
if rafters are exposed, you can use 2X4 or 2X6 with a vertical piece of wood (2X4 or even 3/4" plywood) lapped onto joist and rafter to break the span.)
i would do this regardless of framing member, as 12' is a long span.
if hanging off existing ceiling, it all depends on what's up there...
i would also discourage use of sheetrock on a porch.