here is what i found: old screwdrivers get magnetized better, i dont know why, probably because they contained more steal, apart from the newer ones that have other metals in there composition.
if i remember well someone told me that on some screwdrivers says "non magnetizing" or something like this and so you cant magnetize them.
i also found out trying more ways to magnetize them, that you magnetize them faster with less windings and more current then with more windings, from a relay coil, and less current.
my advice is to take some insulated bell wire and wire turn near turn from one end to another and the back to the other end and put is at a suply, maybe have some load in series with it so you will have somewere around 1A and maybe even more, but you might overheat the wire and the insulator will melt.