To give select students an alternative due date or assignment availability, you will need to manage their special access. To do this, click on the "Course Admin" tab in the blue navbar on the course homepage.
Then scroll down to "Assignments" under the "Assessment" section.
Scroll to the assignment you want to give special access to and click the caret next to it, then click on "Edit Assignment."
On the right side of the page, click on "Availability Dates & Conditions"
Then click on "Manage Special Access"
Then click on "Add Users to Special Access"
From here you can edit start/end dates and due dates for select users. Click the blue "Save" button when finished.