There is a Children's Day and it is celebrated on different dates depending on a country and with varying customs. Major global variants include a Universal Children's Day on November 20th, by United Nations recommendation.
No there isn't but I think if we are really honest there is a researn why there is a day for both your parents and it's because they are alway's trying really hard and working for us. I kind of count christmas as My day "children day". Hope this helps!