As a general rule you can deduct expenses associated with any gathering you have for the parents of the children in your program.
Expenses for a barbeque include: grill, tent for shade, water slide, food, napkins, tablecloth, beer, etc. If the items were purchased and used only for the event (food, tent and water slide rental) you can deduct 100% of the cost. If the items were used for personal purposes after the event (grill, water slide that was purchased, not rented) deduct your time-space % of the cost.
List these expenses under “Advertising” on Schedule C.