Are there anti-greenhouse gases? The Greenhouse Effect can be described semi-formally as follows:


With no atmosphere, virtually all of the heat received by the Sun would be radiated back into space at night.  This can be seen on the moon, for example.
Atmospheric gases have a "greenhousivity" property that traps heat and holds it in.  Some gases have more greenhousivity than others.
Let the value of the weighted average of the greenhousivity values for the mixture of gases commonly known as "air" be arbitrarily defined as 100.
There exist certain gases whose greenhousivity value is so much higher than 100 that adding even a few parts per million to our atmosphere--far below any threshold that would make the air unsafe to breathe--can raise the heat retention of our atmosphere by a non-trivial amount.  These are known as "greenhouse gases".  The two best-known examples are carbon dioxide and methane.


With this understanding, an interesting question arises.  Because 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.  "Anti-greenhouse gases," if you will.  So what's stopping us from pumping a few parts per million of anti-greenhouse gases--some of which are normal parts of air, that we're already well-equipped to breathe--into the atmosphere to counteract the influence of greenhouse gases?
Fundamentally your reasoning is flawed because the major composition of the atmosphere is nitrogen and oxygen.  "Pumping a few parts-per-million" of some other gas into the atmosphere won't do anything to the relative contribution of GHGs to global warming.  GHG's contributions will still be felt the same, regardless of the presence of any other gas.  The "anti-greenhouse gas" that you refer does not exist.  All gases scatter and absorb different wavelengths of light in unique ways, and this all varies by temperature. However, no gas destroys light energy.  A realistic answer is to increase clouds and aerosols, which will reflect more energy back to space before it can be absorbed by the Earth's surface.  

Humans now account for the majority of greenhouse gases in our atmosphere.  Regardless if we shut off all our GHG emissions, our climate will still be warm for at least the next century.  Realistic solutions to reduce climate warming include:


grow massive tree farms; increase algae production and forest cover.
stop emission sources
cover disturbed and urban surfaces (and rooftops) in reflective color/material
cloud-seeding (which can also increase snow-cover)
Injecting aerosols/particles into the stratosphere to mimic a major volcanic event