This is really difficult since the Edwardian period lasted only a very short time. How about the old fashioned bathing costumes? A baggy striped T-shirt, some cut down leggings just above the knee, and, for a girl, an elasticated mop cap - and for a boy, a false moustache.
For girls - long skirt , blouse and shawl or jacket
For boys knee length trousers, long socks, shirt/jumper and a jacket/waistcoat
Edwardian was not disimilar to victorian without the crinolines
You could dress the girls as suffragetts(purple)or maids in service The boys in Khaki (Boer War) or boy scouts which were founded in that period. Hope this info helps.