I'm not sure how old my Black & Decker CM600 Cordless mower is, but it was old enough that when I went online to look for the part I needed, it was obsolete. I wanted to keep the mower working because I had just replaced the battery earlier in the season and I wasn't going to let a little wheel problem make me purchase a brand new mower. So, time to break out some tools and create a DIY fix.
The original part that broke, was a piece of plastic that covered the right rear wheel arm and provided a bushing for the wheel (over a steel axle).
In the two pictures (with the wheel removed), you can see how the bushing was supposed to work. The bushing was molded to the part of that assembly that's closest to the mower deck. And the retaining ring would have been pushed up close to the wheel hub over the bushing to hold the wheel on. The second picture shows the metal axle that's under the bushing (it was taken after I drilled and tapped the hole in the end).
With the bushing section broken, the retaining ring would no longer hold the wheel on, so my idea is to drill and tap a hole in the end of the axle and use a screw and washers to hold the wheel on. The next few sections assume that you're already familiar with the use of all the tools listed.