When I finally got rid of my last car, I was losing around 15psi per day due to the rims being way past their prime. 90's factory alloy rim.
Having gone through this, some notes:
You might be able to save time and aggravation by asking around for places that specialize in rim repair\resurfacing.
Most tire shops will write it off as a bad bead or something that they will basically charge you $$$$ to throw sealer at the issue. what will happen is that you will be fine for a few days or weeks and then the leaks are back to what they were before. They will do minimal inspection and do their best to get you out the door.
Some tire shops will try the old "just grab something" around the shop and smooth it out technique. they do the water test, yank the tire and try and smooth out the surface where it was leaking....THEN slap on a bunch of bead sealer and hope it goes away. the intentions are good. The issue is the competence is not.
What you want to do is find a shop and then locate the old guy at the shop. Let them know that you have a issue a slow leak and you think it might be a corroded alloy issue. At that point they will pull it, clean it up and inspect the entire rim. Not just the spot where its leaking. I'm not sure of the latest and greatest technique but I think it may be sandblasting followed by polishing with a certain types of compounds. If done properly the rim should be good for the long haul. On my old car the only rim that wasn't leaking was the one I had repaired years earlier.
Depending on the cost and current condition of the rims, you should also keep an eye on local salvage yards and craigslist.
Tons of peoples give up OEM rims for cheap.