Going outdoors to shoot portraits of children seems much more natural to me than being in a studio. I like to fit portraits into a scene. With a little planning you can create beautiful images. People have beautiful gardens that can be used or try local parks.
Look for nice even lighting, open shade is ideal. Under trees, arches in the shadow side of buildings.
I particularly look to reflect seasons, the first photograph was taken in a local park. You need to have good communications with the family to organize the shoot and type of clothes. The autumnal colors of the leaves in the foreground is reflected in the child’s clothes.
Rather than leave shots to chance, plan to get the child in the right place you want to shoot. Then let them be children. Let them behave naturally.
They only have a short attention span so get the shots quickly and move on to the next spot. Make the shoot as much about play as the photography as you can.
Make sure that you take a variety of shots from full length to close ups of the face. Remember that you are satisfying not only the parents but grandparents. All will like different shots so offer variety particularly if you are looking to sell and maximize sales.
The shot below is one from a walk through a park. Not traditional as the little girl is facing away from the camera. Nevertheless it is endearing as you see her face as she carries her dog. It would make a lovely piece of wall art for people rather than a close up of a face.