Harris silbright and Harris flux will allow you to soft solder copper to stainless. Don't get the stainless too hot or the solder will just ball up and run off, getting the copper hot and letting that heat transfer into the stainless is the easiest way to do it.

55% silver and the silver solder flux (white) will do it as well and requires less heat. Harris also has a silver bearing solder out that has the flux already in the rod, its a very easy product to use but fairly spendy.

I always use the "Sil-bright" as its the cheapest option and I already have a roll. I have used the silver bearing rods with flux in them and like it a lot, but at 60 dollars for a half a dozen foot long sticks it is a little spendy for my tastes. It does work well though.