If the volume is not going to be ridiculously large, I'd probably create a table that logs each event individually, with a DateTime as @Turnkey suggests, and possibly the machine that logged it, etc.
LOGID (PK) ACTIVITYID SOURCE DATELOGGED
---------- ---------- ------ ----------
That would give you the ability to run a query to get the current count, and also to use the data to determine events in a time period, and/or coming from a specific machine. A clustered index on ActivityID should give you good query performance, and the table is narrow so inserts shouldn't be too costly.