A child with laryngospasm can be a scary thing to manage. There's no way to predict whether a child is going to get it.
You can try the usual maneuvers including a jaw-thrust, positive pressure ventilation to try to open the vocal cords, and suctioning. If these don't work, you might consider giving the patient a paralytic, such as succinylcholine, and performing an endotracheal intubation for worsening hypoxia. Before that, what non-invasive maneuver can you try first?
Trick of the Trade: Laryngospasm notch maneuver
This maneuver, mentioned in the anesthesia literature, is more based on a single physician's longitudinal experiences (Dr. Philip Larsen, Professor of Clinical Anesthesiology at UCLA). Anecdotally, many pediatricians and anesthetists use it. I haven't found any published studies on this maneuver though. Interestingly though, I've found it mentioned in 2 EM blogs by Life In The Fast Lane and Dr. Bearemy from earlier this year. Better late than never for me, I suppose.
Firmly push the soft tissue just behind the earlobes of the patient's ears. Be sure not to go too inferiorly along the ramus of the mandible. You want to push at a point as superior as you can go in this notch. Push both sides firmly inward towards the skull base. Simultaneously, push anteriorly similar to a jaw-thrust maneuver. This should break the laryngospasm within 1-2 breaths.
It's unclear about the mechanism behind why this works. Here are some theories
Read the original online commentary by Dr. Philip Larson in the Anesthesiology journal.