I have a table (x) with fields (serial number, serial number assign date) and a second table (y) which is a child table wherein I need to automatically select the next available (where serial number assign date = null) serial number from (x).
Please provide more details. Are you working in a Formula field? Or a Pipeline?
This kind of thing has been difficult for me in the past, because the Quickbase Formula functions fall a little short for tasks like this. It usually ends up being complicated, as you often need to set up companion fields to track data, or even a related table just for tracking sequence info and "next" id. I have messed around with this kind of thing for creating auto-numbering customer managed ID fields in sequence, and it is tricky.
But, depending on your situation it may not be that hard... can't say without more details and knowing your exact infrastructure.