First things first,
the value of 100 for the greenhousivity of standard air is an average
for a mixture of gases, this necessarily implies the existence of
gases with a value less than 100.
This isn't a good way to look at the greenhouse effect. I mean no offense, but it's simply not accurate.
To get a more realistic understanding, you have to look at reflection and wavelength, and/or by looking at the Earth's energy balance.
Most of our heat comes from the sun, but a smaller share comes from the internal heat of the earth, but the internal heat from inside the earth is reasonably consistent and can be ignored for the sake of this argument. Stored heat is also important, and that, for example, explains why the lowest sunshine day of the year (December 21) isn't the coldest day of the year, but to keep this reasonably short, lets ignore stored heat too.
The heat in / heat out balance works kind of like this (from the link above):
71% of the energy we get from the sun warms the earth, 29% is directly reflected back into space.
Of that 71, 59 is returned to space from the atmosphere and just 12 is returned to space from the surface. That's the atmospheric blanket effect in a sense. Most of the heat, in the form of infra-red light has to travel through the atmosphere to leave the earth and the greenhouse effect reflects that light, just like colored dye in water reflects light, where clear water mostly lets light pass through it.
Atmospheric circulation plays a role too, so do clouds, but lets ignore that for now as well. The greenhouse effect, caused by CO2 or other greenhouse gas, H20 or CH4 (H20 in clouds is different, that's tiny ice particles), but water vapor, which, in the air is invisible to our eyes. They work in essentially the same way as putting colored dye in water, the colored water absorbed and reflects more light than clear water, and the sky, to infrared light, is opaque with greenhouse gas. That Opaqueness can only be removed by reducing the amount of greenhouse gas. It can't be removed by adding other gas, so the greenhouse effect is essentially, directly tied to the amount of greenhouse gas in the atmosphere.
What Greenhouse gas does is it affects the 12% and 59%, and the rate and way that heat leaves the earth. If heat leaves the earth more slowly, the earth gradually warms.
What "global cooling" gases do, doesn't undo what greenhouse gas does. That's not possible, any more than it's possible to make a dye in water stop being opaque by adding another color.
Global cooling gases do exist, but they work in a different way, by affecting the 71%-29% ratio. Volcanic gas, for example, raises the 29% of immediate reflection and that cools the earth. Volcanic cooling however is quite temporary, lasting a few years at most, but that's basically the gist of your question, is, what reflective to visible light gases can be used to raise the 29% so that the thicker blanket of greenhouse gas is counteracted, and that's a perfectly valid question.
There's 3 problems.
The first is, when you talk a few parts per million in the entire atmosphere, you're talking billions and billions of tons. inserting billions and billions of tons of gas into the atmosphere is no simple task.
The 2nd problem is, atmospheric half life. CO2 has a very long half-life in the atmosphere. Your average CO2 molecule that enters the atmosphere takes over 100 years to recycle back either by photosynthesis or by oceanic absorption. It stays in the atmosphere a long time. CH4 has a much shorter half life, of just a few years, and that's the case for many gases, so if you attempt to cool the earth using a global cooling gas, you'd need to replenish it every few years (billions of tons every few years), that gets expensive.
The 3rd problem is many "global cooling" gases are gases we don't want in the atmosphere like SO2, which creates acid rain. I don't think anyone wants to shoot, (you might not need billions), but tens or hundreds of millions of tons of SO2 in the upper atmosphere every few years just to fight climate change. That would be both expensive and it would cause other problems. Freon has a slight cooling effect because it reduces Ozone, but that's even worse. I looked but couldn't find a list of gasses that cool the earth though I've seen them in the past. If somebody can find one, feel free to post).
Other methods of increasing the 29% reflected, we could perhaps, build orbiting giant mirrors or put reflective surfaces over land or large floating disks in the ocean but none of those methods are easy.
An article on some of the problems with trying to increase the earth's reflection: http://www.theguardian.com/environment/2014/nov/26/geoengineering-could-offer-solution-last-resort-climate-change
It's not talked about as much as reducing CO2, but increasing reflection of solar energy is being explored and studied as a possible or partial solution to man made climate change.
Hope that wasn't too long or wordy. I'll try to clean it up a litte. Corrections welcome.