How could I create a machine that as rapidly as possible creates greenhouse gases from air?
Current concentrations of $\ce{CO2}$ and $\ce{CH4}$ in the atmosphere are around 390 ppmv and 1.75 ppmv, resp. These concentrations and the wish to obtain large quantities of both gases rapidly seem mutually exclusive, unless you use (at least one) additional carbon source. 

Taking the options for interconversion into account, $\ce{CH4}$ in pressurized bottles would be an obvious choice ;).