Unfortunately, that other question is about web maps, which have a much more limited way to symbolize data.
With ArcMap 10, you have quite a few options. You could use graduated or proportional symbols, but that goes back to the color/size method you already mentioned. And truthfully, based on what you are describing, I think some form of chart symbology may be the most useful. You will likely need to create another field in your attribute table in order to get the results you want however.
I would probably populate this new field with integer values that represent the number of overlapping points (E.g., 3 overlapping points gets a value of 3). Then when you symbolize based on this field, your chart will give proportional weight to areas with high/low occurrence of events. A bar or stacked chart will probably display better than a pie chart.
Also, if you are concerned about multiple points trying to display charts at the same X/Y, you could just populate one of the coincidental points with a value and leave the others as zero. Then just use a definition query to not display the zeros, and that leaves all the rest that have >0 values.
By using this method, I'm assuming you aren't trying to distinguish individual events, but mostly trying to show intensity at a location?
It can be very difficult to cleanly show multiple symbols for points that occupy the same spatial location. That's why the other "duplicate" question answers mention clustering. Clustering can look really messy, though, especially if other points are nearby, but not the same X/Y.
Let me know if you need any clarification, or if I didn't answer your question well.