This paper continues the exploration of Machine Learning (ML) parameterization for radiative transfer for the ICOsahedral Nonhydrostatic weather and climate model (ICON). Three ML models, developed in Part I of this study, are coupled to ICON. More specifically, a UNet model and a bidirectional recurrent neural network (RNN) with long short-term memory (LSTM) are compared against a random forest. The ML parameterizations are coupled to the ICON code that includes OpenACC compiler directives to enable GPUs support. The coupling is done through Infero, developed by ECMWF, and PyTorch-Fortran. The most accurate model is the bidirectional RNN with physics-informed normalization strategy and heating rate penalty, but the fluxes above 15 km height are computed with a simplified formula for numerical stability reasons. The presented setup enables stable aquaplanet simulations with ICON for several weeks at a resolution of about 80 km and compare well with the physics-based radiative transfer solver ecRad. However, the achieved speed up when using the emulators and the minimum required memory usage relative to the GPU-enabled ecRad depend strongly on the Neural Network (NN) architecture. Future studies may explore physics-constraint emulators that predict heating rates inside the atmospheric model and fluxes at the top.