historical accuracy - Were children subjected to shock therapy in the 1960s, as implied in Moonrise Kingdom?

If the therapy in question is Electroconvulsive therapy, then yes, it is highly possible that children were given this treatment.

Despite the fact that ECT was allegedly phased out during the 60's and 70's, the treatment continued to be administered, and even gained a little popularity around 20 years ago due to its effectiveness.