Nothing built into ShopSite that would allow them to specify a pickup time. But you could add a comment to the Order Info box or Comment box that says to enter the pickup time in the box.
If you have a Pro level store you could add custom checkout field to give them an option for selecting a pickup time.
Edit: Found out you can do it on the same place you add the custom checkout fields.
Thanks Jim. I was able to add the custom checkout field without any problems. Can you direct me to where I can add this to the email that gets sent to me after I place the order?