I try to engage children by asking them questions....all kinds of questions...their favorite toy, favorite candy, favorite season, etc. Sometimes I get them to sing songs with me ("Old MacDonald" seems to always be a hit for some reason).
There are times when I do have to get the parents involved, especially with very young kids and infants. The problem I have run into is that the parent's first instinct is to stay just to the side of the lens and interact with the baby. I always have to redirect them to stand behind me, so that the child is looking in my direction instead of off to the side. I can't tell you how many times I have actually laid on the floor on my belly and had Mom or Dad standing or straddling over my back, cooing at the baby.