What do you do if there is only a very small area for your newly pierced belly button piercing?

If you mean that there is only a very small amount of skin that the jewelry passes through, it was likely pierced too shallow and will either reject (the body will push it out through the skin like a thorn) or it will simply never heal properly. I would suggest seeking the opinion of another, preferably more reputable, piercer.

If you mean there is only a small area for the jewelry to rest in, as in you have a small belly button, it would be best to consult a professional piercer to find out if you are suited to the piercing.