Thanks so much for your replies on this. We took the advice above and went over to King Architectural Metals in Buena Park. Super nice people. We initially purchased the paint stripper, but with the thickness of the whte paint that had been applied in the 1980's, it would have taken us the entire weekend to get it off, so we gave in on that part and had them sandblasted. Then we picked out the pieces from Kings, and our neighbor welded the pieces on, and then we sprayed it all with rust-oleum painter touch in semi gloss black. Then we sanded down the handrails, and stained them with 3 coats of cherry stain, and we were done. The hole thing cost us about $200.00, and we are very pleased with how it turned out. The sandblasting alone was $125.00, so if your railings are already black, your in great shape and should be able to do this for under $75.00. Good Luck.
Q