Değildiler and değillerdi are apparently both right, but which one is the most apropriate?
It should accept "yoktu" as well as "değildi".
As the plural is already indicated in "çocuklar", can, is it possible to drop the plural from the verb and use "değildi", as one does in the present continuous?
As far as I know, it is always optional to use the third person singular form of the verb if the subject already has the plural marker.
Why is it "değildi" Instead of "değildin"?
Because "değildi" is the third person form. "Değildin" would be the "sen" form. ("You weren't at the park yesterday." -> "Sen dün parkta değildin.")