I am the director of finance for a business that provides music and
dance lessons to children.  I am using Quickbooks Point of Sale.  I
have purchased small cards with bar codes, like you would see at
Safeway, Albertson's or Ralph's.  I would like to use these cards to
store information regarding how many classes a child has at any one
time.

For example, let's say that a parent buys a set of 10 classes for a
child.  The cashier load information onto the card showing that the
child has accrued 10 classes.  Every time that a child comes for a
class, the card is scanned by a barcode reader, and Quickbooks Point
of Sale indicates that this class has been used by the child.  Any
ideas?  What resources can help me?

I don't think you can put information the type of card you described.
What you can do is use the number (barcode) on the card as an ID
number for each child. Then use a database (like MS Access) to track
information about each child and/or each visit. Hope that helps. 
--Noon