Here is a list of the major daycare company's in Amstelveen. You can find a full list here.
If you are looking for a nanny or a child minder, you can find your match through these websites;
When your child reaches the age of 3, you can sign them up to the famous International School of Amsterdam in Amstelveen.
In the category Education al the other elementary and high-schools in Amstelveen are listed.