Master teacher Carolyn Wood applies glue to an art project with student Brendan Compton, 4, at Children’s Discovery Center in Norman on July 24. The childcare facility, which takes children up to 5 years old, is currently full with a waitlist of families hoping to nab a spot.

The unexpected closure of a well-regarded, highly rated child care center in Oklahoma City has put parents in an all-too-familiar, tough spot: scrambling to find places for their children amid a drop in the number of daycares.

For Jennifer Morton, the closure of Oklahoma State University-Oklahoma City’s Child Development...