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Any pressure treated wood rated for ground contact should work well. Using 2 2x6 instead of 1 2x12 would give you better drainage and as Torque1st said frown down. (if you look at the end piece and the rings look like a smile ...turn it over)
Look into TREX, I have used it on numerous decks, it is a great product. A little more expensive, but if you have to replace your current stuff every few years, it is worth the extra $. It comes in 2x6 configuration and several colors.
Is your rotting problem coming from the underside or the topside? If there are drainage problems going into the garage, you might address that issue first. 1x12 TREX would be fine if it is supported enough undernieth, it is kinda bendy.
Doubleing the 1X12 won't give you the strength you need for treads. In fact their 5/4 thick decking requires joists spaced on 12" centers if you install them on a bias. You could laminate them on top of something more substantial like 2 2X 6" to protect the wood from the weather. In that case I would cut 1 1/2" from the bottom of the stair stringer to maintain the oreiginal tread height, otherwise you would have a bottom step that is too short and a top step that is too high.