Your description makes me smile, Betty. Yes, I know exactly what you mean.
That pointy part is called a culet, and the top of the stone is called a table (see below). Traditionally, the culet is the back of the stone, and therefore made as the back of most pendants. To prevent this "point" from scratching skin, the frame needs to go from the top of the stone all the way down to the culet.
An example of how to execute this would be to make the frame, and then push the side frame wires in (about 1/3 of the way toward the back) to hold the bottom of the stone in the frame.
Personally, I have a few stones that have been buff cut, meaning that the top is not faceted, but rounded, and I actually do set them upside-down, culet up. As the designer, the choice is yours!
P.S.: A good example of these type of settings are in the Advanced DVD Series!