You can probably solder some small stainless steel parts with a soldering
iron, Ray, if you can get enough heat to transfer into the workpiece(s).
Harris Stay-Brite #8 silver bearing solder is a low temp (melt 430/flow
530F) solder that can be used on stainless.
The #8 formula is lead-free, tin plus 5-6% silver by weight (about $53/lb
last year, 1/16" dia)
Harris Stay-Clean liquid flux (zinc chloride/hydrochloric acid) will work on
most metals, including stainless, except it's not recommended for aluminum
(or electrical/electronic applications).
You probably realize that typically, stainless alloys don't conduct heat
very well, and soft solders generally aren't exceptionally strong. I suppose
that there would be some strength information on the Harris website.
Click to see the full signature.