I don't know about the cost but you will have to compact the fill to keep from having a sunken area. Is there a base under the rest of the patio stones? The new ones will not be a perfect match in color but if you pressure wash all of the patio it will help it blend in better.

That is a small area, so it shouldn't cost much. The current 'stone' appears to be the standard stuff that Lowes/Home-Depot sells. It isn't expensive. This is something that can be done by hand. I had a stone patio put in by the local semi-experts. It was large enough to require a big truck, but you could get needed stuff in a pickup or a van from a landscape center. If I'm not mistaken, we leveled the land, added an inch or two of gravel and dumped sand on top. I think that they may have had a mechanical vibrating tamper, but for such a small area, you could just use a manual tamper. It is just a heavy flat bottomed piece attached to a handle. Since it is in sand, even if it sinks a little, you could always just remove the bricks, add some more sand and you should be set.

Of course, you could always go lazy, and throw some dirt in there and plant some flowers.