A global text field set up with a value list of day of the week names should work for you. Let's say that field is called gSelectedDayName. I am also assuming that DeliveryDay is a text field and not a date. A different script would be needed if that field is a date field.
Go to Layout [package]
Enter Find mode //clear the pause check box
Set field [Package::Deliveryday ; YourTable::gSelectedDayName]
Set Error Capture [on]
It is possible to perform this scripted find on other layouts not based on the Package table, but then the relationship between that layout's table and package must be one that works for the find you are performing. If that's the case, you'll need to describe your database and layout in more detail.
The script will not work unless gSelectedDayName has global storage specified in field options. It can be defined in any table in your database.
Thanks Phil, I had the script right but like you mentioned i needed to adjust a couple table relationships. It works like a charm now!