Dart in the radiator... How do I fix it without replacing the radiator?
If the radiator is constructed of a material to which solder will adhere (copper, steel, tin), you can scrape away some of the paint surrounding the hole. Because you've turned off the water, careful application of heat, flux and solder will seal off the hole on a permanent basis. Conventional copper plumbing is assembled with solder in a similar manner. A hole as small as one millimeter is easily bridged with solder and will not blow out under household water pressure.

As noted in other comments, discuss this with the owner prior to scraping paint. Obviously, when done, clean the area and repaint.