The Better The Setting, The More Relaxed The Child!
The Setting – If you are lucky enough to have access to a studio with a good lighting set up, and if the parents are after the more formal shots then great. However, for most photographers starting out, this is usually out of the question as the costs and spce required are sometimes quite high. You could always convert your living room or spare bedroom into a temporary, makeshift studio using maybe some second hand studio lights or speedlights with Pocket Wizards and brollies.
I personally think, that with children, there is no better environment than their own home or somewhere that is familiar to them, especially if they are young children. They will be more relaxed in their own environment with their own things around them, especially toys, which you should try and use as props. (Second best, at their school or nursery).
Get the parents to either clear a bit of space, if necessary, or check out their bedrooms to see if they are suitable. If a garden is at your disposal, and it is a nice day, use it! Gardens and lawns are a great place to photograph your child or children, but be prepared to get a little mucky. Make sure that you understand the light and how it affects the shot in each setting as it will tend to differ depending on the mixture of light bulbs and natural, available light.
Failing all of that, arrange to meet the family at their favourite location outdoors or one that you know is quite photogenic and flattering and one that is also appealing to the child and will help them to relax and play. A happy child makes a great subject to photograph.