Strong countersunk ring magnets sized specifically for #2 flat-head screws.
These rings are sold by the pair. One will have the north pole on the side with the large end of the hole and one will have the south pole on that side, so they will attract each other when they are screwed in.
These small countersunk rings can be used for a wide range of applications including closures for cabinet doors and handbags. Also available in grade N42, part number R422CS-P.