To do this turn on the following setting:
  1. In your TeamRaiser go to the "Manage Stationary" step
  2. On this page under "Use Only Event Stationary" choose "Yes, allow Participants to select only Stationery selected for this TeamRaiser event"
This option is not supported in Participant Center Classic.

While binding specific stationary to an event is not allowed for Participant Center Classic, if you edit the messages themselves we should be able to accomplish the same goal with the folloing steps:

        1. Open up the TeamRaiser event under Edit
        2. Go to the "Customize Suggested Messages." step
        3. Edit the specific message
        4. Navigate to Message Stationery and preselect a stationary to use for the message.

This will take some extra configuring ahead of time, but if every message is set up this way then you'll be able ensure that only the intended stationary is used.