Two sources for keyslotted shaft stock are
MSC and
McMaster-Carr. And there are lots of others.
The most common method to cut the keyway on the interior of a gear or wheel hub is to use a broach set. This is basically a specialized set of cutting blades (think of it as a very wide saw blade with just a few, large teeth) that are forced through the bore opening with an arbor press (a manual press will work just fine). Two passes with the broach, and you are all set. You can buy individual broaches, or complete sets, from either of the sources mentioned above. If you can't afford broaches (a full set can be $150 - $300), you can cut keyways with the lathe, it just takes some patience. Put the gear in the lathe chuck, and lock the lathe spindle with the backgear so it doesn't rotate. Mount a small square cutter in a boring bar, and put the bar on the lathe cross slide (sort of like a sharp tooth on the end of a stick). Advance the cross slide carriage toward the spindle, and let the cutter just skim the inside of the gear bore. Retract the carriage, advance the cross slide a few mils, and do it again. Repeat until you have cut a keyway of the correct depth (1/2 the width of the key). It takes a while, but it works.
Note that if you cut a shaft keyway that is too large, you may substantially weaken the shaft/axle. The industry rule of thumb is that the keyway width should be no more than 1/4 the diameter of the shaft.
Most common keystock falls in the range of 35,000-50,000 psi shear strength. Based on the dimensions of the key you use, and the radius of the shaft, you can calculate the maximum loads the key will withstand before it deforms and shears. Make sure you size the key appropriately, otherwise you may end up shearing through them just as you did with the pin mounting (although at a much higher load level).
-dave