Why is Carbon Dioxide a Greenhouse Gas whereas Ammonia is not?
A molecular gas is a good infrared absorber if it has several atoms (not just 2, like O2 and N2) or if it is hetero-nuclear (e.g. CO and NO).  These type of molecular arrangements allow more infrared energy to be absorbed because there are more vibrational states that are possible.  Yes, ammonia fits that description, but it is not long-lived in the atmosphere and it is not widespread.  So, even though ammonia is a good infrared absorber, it is not an important greenhouse gas.

Ammonia in the atmosphere is very reactive, and will form to make nitrates and sulfates while in solution (e.g. in cloud droplets).  Thus, the atmospheric lifetime of ammonia is short-lived, whereas most important greenhouse gases are long-lived and not reactive.  For global  warming discussion, you would likely associate ammonia with a net cooling effect since the increased formation of particulate (clouds/haze) increases the albedo of the Earth (which scatters light back to space).