Can be confusedchildish childlike (see synonym study at the current entry)
Examples from the Web for childishly
The British are too undisciplined to be good at what they are most (regrettably and childishly) interested in.
Bachelor couples breaking up is nothing new, but few have it out as publicly and childishly as Jake Pavelka and Vienna Girardi.
Here is a little game that is childishly simple in its conditions.Amusements in Mathematics|Henry Ernest Dudeney
When all was still he spoke again, and the tone of his voice was childishly wistful.A Woman's Will|Anne Warner
But otherwise she was ignorant, beautifully, childishly ignorant—and undismayed.Septimus|William J. Locke
This childishly amicable system, which is as clumsy as the block-houses erected, can be developed on much finer lines.The Jewish State|Theodor Herzl
She was of a sanguine and buoyant disposition, childishly fond and playful, ready to laugh at anything, loving to talk nonsense.Byron|Richard Edgcumbe