Hi Rebecca,

Probably the best method is to Edit the Quiz, go to the bottom where the Assign section is and click the + Add button.  This lets you add one or more students and set a different due and availability dates.  Do not remove the Everyone from above this but notice it should change to Everyone Else when you add a 2nd set of dates.  This page tells a little bit more about the process https://community.canvaslms.com/docs/DOC-9973-4152101242 

Rick