Can't update trigger because of activity
When you issue an ALTER TRIGGER statement, that process will attempt to acquire a SCH-M (schema modification) lock on the table object as well as the trigger object.  This is an extremely low-concurrency lock and will cause the expected blocking that you're running into.

See this reference for a chart on lock compatibility.  For referencing sake, here is the chart linked directly from that document:



As you can see, that SCH-M lock will conflict and cause a concurrency blocker.

Much like anything that can cause an interruption, or be blocked itself, I'll have to agree with the comment above (from David Crowell).  You simply need to find a time when there is little to no activity on these objects.