RunSignUp allows you to set up protected registration, which will let you create a password that all registrants will be required to enter in order to sign up.
Setup Password Protected Registration
To setup a password protected registration, you can select Race > Display > Protected Registration
You can then set a start date and end date for when this particular password is in effect
You can then set and confirm your password.
You can use the Add Another Password to add additional passwords for additional periods.