I wholeheartedly agree with Nate Eldridge that the best thing to do is to seek the advice of an immigration lawyer before doing this. However let me give you my understanding, having recently had a relative go through something very similar.
If you say at immigration that the child is coming to live with you, and you have no papers proving that they have a visa that allows them to do so, then you run the serious risk that they will be turned away at the border, and that you have an entry on your record saying that you attempted to facilitate an illegal entry into the US.
On the other hand, if the child comes to visit you for the amount of time that they are legally allowed to do without a visa, that is perfectly fine. If you then change your mind and apply for a change of status while they are there, so the child can stay with you permanently, that is also fine. However to back up your statement that they are coming to visit you, you should have a plan to return the child where they came from before the allowed time is up. A return ticket would be good evidence of that, though it may not be necessary if you have other evidence. You might want to plan for schooling the child during a temporary visit, in order to demonstrate you have thought about it. If immigration suspects that you are bringing the child specifically to live with you, that would be a problem, and might get you the same penalties as above.
But really, a lawyer would give you a much better answer on this.