How do you keep the heat from rising from a gas fireplace?

You cannot defy the laws of physics however If you are lucky, I may have a solution. If your heating system has return air vents which can be opened and closed, try closing some of the ones downstairs and leave your furnace fan run constantly. This will pick up the warm air upstairs and redistribute it through the home.

If you have high and low sidewall return grilles, all the better because they probably have shutoff dampers built in for this purpose. You would alternately close upper or lower return vents depending on heating or cooling needs. It may even be possible to add high sidewall return vents depending on your home's construction.

Is it a vent-free fireplace or direct vent fireplace? If it is vent-free they do not radiate heat well at all. Just because of the design and the way they have to burn all of that heat rises very fast. A good direct vent fireplace radiates the heat out so you can actually feel the heat on the level where it is located. Although, eventually that heat will rise too. I would recommend a direct vent unit such as a Fireplace Xtrordinair.

We have a very similar situation in our house. We finally invested in a couple of box fans to pump the air around from the higher levels. It definitely gets the air moving and does seem to even out the temperature, but I think the upper level is still fairly warm. Good Luck!

Install a heatalator or blowers to direct the heat to a lower level. That's the only way I know.

use a fireplace fan to blow the heat outward