You can use the Watches toolbox for this. It does almost exactly what you are suggesting with the Events toolbox. A watch has a name and a value and basically represents an item in your application code which changes over time. The item is typically a variable (think database connection count e.g.), but could also include other things like the count of fired events.
There are currently methods in the libraries for sending watches of type String, DateTime, Integer, Float, Boolean and more (see the documentation of the TSiSession.Watch method for details). The mentioned Watches toolbox displays these watches in a key/value list and signals changes (new or updated watch) with a red icon. To simulate the requested behavior, you could use the WatchInteger method. The first parameter of this method would be the name of the event and the second parameter specifies the event count.
Because of your posting, we plan to add a method called something like WatchCounter which takes a single string parameter and automatically increments the count for a particular watch. Thanks for the nice idea.