My 1995 car has aluminum rims and my new tires leaked air despite two different garages cleaning and remounting them. Road salt is a problem here too. I finally bought a can of air with sealer in it. The first can I bought had a screw on adapter. It broke when I tried to screw it on. Then I tried a can with a press on adaptor and it worked great. No more air leaks.
If I had the tires off, I'd paint the insides of the rims are suggested, but if it still leaked I try a can of air. They also sell the sealer called "slime" at Walmart, but the tires have to be empty to pour it in.