Convective adjustment and diffusive schemes based on terrestrial methods are extended to outer planet applications in order to develop an algorithm that can be used in dynamical modeling of outer planetary flows. Over the temperature range between 50 K and 250 K the delayed conversion of ortho- hydrogen to para-hydrogen can have large effects on stratification. One-dimensional modeling of atmospheric layers cooled from the top, as by radiation to space, is reported. After ortho- and para-hydrogen are mixed by a convective event, the ortho/para ratio begins to relax toward thermodynamic equilibrium. The energy release during relaxation drives the atmosphere toward stability. On Jupiter, the influence of hydrogen conversion on convection is small. On Neptune the energy released by hydrogen conversion is large, and it shuts off convection. A time dependent structure ensues, with irregular occurrence of mixing events associated with temperature fluctuations of 1 K or more. The mean thermal structure at levels where the temperature is less than about 250 K is significantly stable, in contrast to the predictions of conventional outer planet radiative-convective calculations.